Housing Prices Regression Kaggle Competition

Date Created: Sunday 19th April 2020
Author: Scott Jenkins
Contact: https://www.linkedin.com/in/sjenkins97/
Date Modified: Saturday 16th May 2020

Brief:

In this notebook I apply linear regression models to predict house prices in this Kaggle competition: https://www.kaggle.com/c/house-prices-advanced-regression-techniques/overview|

Ask a home buyer to describe their dream house, and they probably won't begin with the height of the basement ceiling or the proximity to an east-west railroad. But this playground competition's dataset proves that much more influences price negotiations than the number of bedrooms or a white-picket fence.

With 79 explanatory variables describing (almost) every aspect of residential homes in Ames, Iowa, this competition challenges you to predict the final price of each home.

Contents:

Importing Libraries

In [2]:
import pandas as pd
import numpy as np
import statistics

# Ignore Warnings
import warnings
warnings.filterwarnings("ignore")

# View All Columns
from IPython.display import display
pd.options.display.max_columns = None

# Visualisation
import seaborn as sns
import matplotlib.pyplot as plt
%matplotlib inline
import plotly.express as px
import plotly.graph_objects as go
import plotly.offline as pyo
pyo.init_notebook_mode()
from simple_colors import *

# Linear Regression
from sklearn import preprocessing, metrics
from sklearn.metrics import mean_squared_error, r2_score
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression, Ridge, Lasso, ElasticNet
import statsmodels.formula.api as smf

Importing Data

This dataset details the house prices of residential properties in Ames, Iowa, United States. There are 79 explanatory variables for condsideration.

Train contains 1460 properties; Test contains 1459 properties the sale prices of which I aim to predict.

In [3]:
train = pd.read_csv(r'C:\Users\sjenkins\OneDrive - Dunelm (Soft Furnishings) Ltd\Documents\Side_Projects\House_Price_Regression\train.csv')
test = pd.read_csv(r'C:\Users\sjenkins\OneDrive - Dunelm (Soft Furnishings) Ltd\Documents\Side_Projects\House_Price_Regression\test.csv')
In [4]:
print('Train has', train.shape[0], 'rows and', train.shape[1], 'columns.')
print('Test has' , test.shape[0], 'rows and', test.shape[1], 'columns.')
Train has 1460 rows and 81 columns.
Test has 1459 rows and 80 columns.
In [5]:
train.head()
Out[5]:
Id MSSubClass MSZoning LotFrontage LotArea Street Alley LotShape LandContour Utilities LotConfig LandSlope Neighborhood Condition1 Condition2 BldgType HouseStyle OverallQual OverallCond YearBuilt YearRemodAdd RoofStyle RoofMatl Exterior1st Exterior2nd MasVnrType MasVnrArea ExterQual ExterCond Foundation BsmtQual BsmtCond BsmtExposure BsmtFinType1 BsmtFinSF1 BsmtFinType2 BsmtFinSF2 BsmtUnfSF TotalBsmtSF Heating HeatingQC CentralAir Electrical 1stFlrSF 2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath HalfBath BedroomAbvGr KitchenAbvGr KitchenQual TotRmsAbvGrd Functional Fireplaces FireplaceQu GarageType GarageYrBlt GarageFinish GarageCars GarageArea GarageQual GarageCond PavedDrive WoodDeckSF OpenPorchSF EnclosedPorch 3SsnPorch ScreenPorch PoolArea PoolQC Fence MiscFeature MiscVal MoSold YrSold SaleType SaleCondition SalePrice
0 1 60 RL 65.0 8450 Pave NaN Reg Lvl AllPub Inside Gtl CollgCr Norm Norm 1Fam 2Story 7 5 2003 2003 Gable CompShg VinylSd VinylSd BrkFace 196.0 Gd TA PConc Gd TA No GLQ 706 Unf 0 150 856 GasA Ex Y SBrkr 856 854 0 1710 1 0 2 1 3 1 Gd 8 Typ 0 NaN Attchd 2003.0 RFn 2 548 TA TA Y 0 61 0 0 0 0 NaN NaN NaN 0 2 2008 WD Normal 208500
1 2 20 RL 80.0 9600 Pave NaN Reg Lvl AllPub FR2 Gtl Veenker Feedr Norm 1Fam 1Story 6 8 1976 1976 Gable CompShg MetalSd MetalSd None 0.0 TA TA CBlock Gd TA Gd ALQ 978 Unf 0 284 1262 GasA Ex Y SBrkr 1262 0 0 1262 0 1 2 0 3 1 TA 6 Typ 1 TA Attchd 1976.0 RFn 2 460 TA TA Y 298 0 0 0 0 0 NaN NaN NaN 0 5 2007 WD Normal 181500
2 3 60 RL 68.0 11250 Pave NaN IR1 Lvl AllPub Inside Gtl CollgCr Norm Norm 1Fam 2Story 7 5 2001 2002 Gable CompShg VinylSd VinylSd BrkFace 162.0 Gd TA PConc Gd TA Mn GLQ 486 Unf 0 434 920 GasA Ex Y SBrkr 920 866 0 1786 1 0 2 1 3 1 Gd 6 Typ 1 TA Attchd 2001.0 RFn 2 608 TA TA Y 0 42 0 0 0 0 NaN NaN NaN 0 9 2008 WD Normal 223500
3 4 70 RL 60.0 9550 Pave NaN IR1 Lvl AllPub Corner Gtl Crawfor Norm Norm 1Fam 2Story 7 5 1915 1970 Gable CompShg Wd Sdng Wd Shng None 0.0 TA TA BrkTil TA Gd No ALQ 216 Unf 0 540 756 GasA Gd Y SBrkr 961 756 0 1717 1 0 1 0 3 1 Gd 7 Typ 1 Gd Detchd 1998.0 Unf 3 642 TA TA Y 0 35 272 0 0 0 NaN NaN NaN 0 2 2006 WD Abnorml 140000
4 5 60 RL 84.0 14260 Pave NaN IR1 Lvl AllPub FR2 Gtl NoRidge Norm Norm 1Fam 2Story 8 5 2000 2000 Gable CompShg VinylSd VinylSd BrkFace 350.0 Gd TA PConc Gd TA Av GLQ 655 Unf 0 490 1145 GasA Ex Y SBrkr 1145 1053 0 2198 1 0 2 1 4 1 Gd 9 Typ 1 TA Attchd 2000.0 RFn 3 836 TA TA Y 192 84 0 0 0 0 NaN NaN NaN 0 12 2008 WD Normal 250000
In [6]:
test.head()
Out[6]:
Id MSSubClass MSZoning LotFrontage LotArea Street Alley LotShape LandContour Utilities LotConfig LandSlope Neighborhood Condition1 Condition2 BldgType HouseStyle OverallQual OverallCond YearBuilt YearRemodAdd RoofStyle RoofMatl Exterior1st Exterior2nd MasVnrType MasVnrArea ExterQual ExterCond Foundation BsmtQual BsmtCond BsmtExposure BsmtFinType1 BsmtFinSF1 BsmtFinType2 BsmtFinSF2 BsmtUnfSF TotalBsmtSF Heating HeatingQC CentralAir Electrical 1stFlrSF 2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath HalfBath BedroomAbvGr KitchenAbvGr KitchenQual TotRmsAbvGrd Functional Fireplaces FireplaceQu GarageType GarageYrBlt GarageFinish GarageCars GarageArea GarageQual GarageCond PavedDrive WoodDeckSF OpenPorchSF EnclosedPorch 3SsnPorch ScreenPorch PoolArea PoolQC Fence MiscFeature MiscVal MoSold YrSold SaleType SaleCondition
0 1461 20 RH 80.0 11622 Pave NaN Reg Lvl AllPub Inside Gtl NAmes Feedr Norm 1Fam 1Story 5 6 1961 1961 Gable CompShg VinylSd VinylSd None 0.0 TA TA CBlock TA TA No Rec 468.0 LwQ 144.0 270.0 882.0 GasA TA Y SBrkr 896 0 0 896 0.0 0.0 1 0 2 1 TA 5 Typ 0 NaN Attchd 1961.0 Unf 1.0 730.0 TA TA Y 140 0 0 0 120 0 NaN MnPrv NaN 0 6 2010 WD Normal
1 1462 20 RL 81.0 14267 Pave NaN IR1 Lvl AllPub Corner Gtl NAmes Norm Norm 1Fam 1Story 6 6 1958 1958 Hip CompShg Wd Sdng Wd Sdng BrkFace 108.0 TA TA CBlock TA TA No ALQ 923.0 Unf 0.0 406.0 1329.0 GasA TA Y SBrkr 1329 0 0 1329 0.0 0.0 1 1 3 1 Gd 6 Typ 0 NaN Attchd 1958.0 Unf 1.0 312.0 TA TA Y 393 36 0 0 0 0 NaN NaN Gar2 12500 6 2010 WD Normal
2 1463 60 RL 74.0 13830 Pave NaN IR1 Lvl AllPub Inside Gtl Gilbert Norm Norm 1Fam 2Story 5 5 1997 1998 Gable CompShg VinylSd VinylSd None 0.0 TA TA PConc Gd TA No GLQ 791.0 Unf 0.0 137.0 928.0 GasA Gd Y SBrkr 928 701 0 1629 0.0 0.0 2 1 3 1 TA 6 Typ 1 TA Attchd 1997.0 Fin 2.0 482.0 TA TA Y 212 34 0 0 0 0 NaN MnPrv NaN 0 3 2010 WD Normal
3 1464 60 RL 78.0 9978 Pave NaN IR1 Lvl AllPub Inside Gtl Gilbert Norm Norm 1Fam 2Story 6 6 1998 1998 Gable CompShg VinylSd VinylSd BrkFace 20.0 TA TA PConc TA TA No GLQ 602.0 Unf 0.0 324.0 926.0 GasA Ex Y SBrkr 926 678 0 1604 0.0 0.0 2 1 3 1 Gd 7 Typ 1 Gd Attchd 1998.0 Fin 2.0 470.0 TA TA Y 360 36 0 0 0 0 NaN NaN NaN 0 6 2010 WD Normal
4 1465 120 RL 43.0 5005 Pave NaN IR1 HLS AllPub Inside Gtl StoneBr Norm Norm TwnhsE 1Story 8 5 1992 1992 Gable CompShg HdBoard HdBoard None 0.0 Gd TA PConc Gd TA No ALQ 263.0 Unf 0.0 1017.0 1280.0 GasA Ex Y SBrkr 1280 0 0 1280 0.0 0.0 2 0 2 1 Gd 5 Typ 0 NaN Attchd 1992.0 RFn 2.0 506.0 TA TA Y 0 82 0 0 144 0 NaN NaN NaN 0 1 2010 WD Normal

Data Cleaning

Before building models, it is necessary to clean our data - removing outliers, handling missing values, and removing collinear features.

Outline Approach:

  1. Check for and remove any outliers from training set.
  • Check for skew and transform target variable (House Price) to have Normal Distribution.
  • Concatenate Train and Test sets to create a single frame to clean. Note that this is the easiest and quickest way to ensure that my train and test sets have the same features after cleaning.
  • Handle missing values through dropping columns or data imputation as appropriate.
  • Check for correlation between independent variables and remove any with high (> 0.9) collinearity.
  • Consider binning categorical variables to create more helpful features.
  • Apply one-hot encoding on categorical variables.
  • Split clean frame back into train and test splits.

It is good practice to scale numerical features to obey a Gaussian (0,1). This is often performed as part of model building.

1. Check for and remove any outliers from training set.

In [7]:
train.describe().T
Out[7]:
count mean std min 25% 50% 75% max
Id 1460.0 730.500000 421.610009 1.0 365.75 730.5 1095.25 1460.0
MSSubClass 1460.0 56.897260 42.300571 20.0 20.00 50.0 70.00 190.0
LotFrontage 1201.0 70.049958 24.284752 21.0 59.00 69.0 80.00 313.0
LotArea 1460.0 10516.828082 9981.264932 1300.0 7553.50 9478.5 11601.50 215245.0
OverallQual 1460.0 6.099315 1.382997 1.0 5.00 6.0 7.00 10.0
OverallCond 1460.0 5.575342 1.112799 1.0 5.00 5.0 6.00 9.0
YearBuilt 1460.0 1971.267808 30.202904 1872.0 1954.00 1973.0 2000.00 2010.0
YearRemodAdd 1460.0 1984.865753 20.645407 1950.0 1967.00 1994.0 2004.00 2010.0
MasVnrArea 1452.0 103.685262 181.066207 0.0 0.00 0.0 166.00 1600.0
BsmtFinSF1 1460.0 443.639726 456.098091 0.0 0.00 383.5 712.25 5644.0
BsmtFinSF2 1460.0 46.549315 161.319273 0.0 0.00 0.0 0.00 1474.0
BsmtUnfSF 1460.0 567.240411 441.866955 0.0 223.00 477.5 808.00 2336.0
TotalBsmtSF 1460.0 1057.429452 438.705324 0.0 795.75 991.5 1298.25 6110.0
1stFlrSF 1460.0 1162.626712 386.587738 334.0 882.00 1087.0 1391.25 4692.0
2ndFlrSF 1460.0 346.992466 436.528436 0.0 0.00 0.0 728.00 2065.0
LowQualFinSF 1460.0 5.844521 48.623081 0.0 0.00 0.0 0.00 572.0
GrLivArea 1460.0 1515.463699 525.480383 334.0 1129.50 1464.0 1776.75 5642.0
BsmtFullBath 1460.0 0.425342 0.518911 0.0 0.00 0.0 1.00 3.0
BsmtHalfBath 1460.0 0.057534 0.238753 0.0 0.00 0.0 0.00 2.0
FullBath 1460.0 1.565068 0.550916 0.0 1.00 2.0 2.00 3.0
HalfBath 1460.0 0.382877 0.502885 0.0 0.00 0.0 1.00 2.0
BedroomAbvGr 1460.0 2.866438 0.815778 0.0 2.00 3.0 3.00 8.0
KitchenAbvGr 1460.0 1.046575 0.220338 0.0 1.00 1.0 1.00 3.0
TotRmsAbvGrd 1460.0 6.517808 1.625393 2.0 5.00 6.0 7.00 14.0
Fireplaces 1460.0 0.613014 0.644666 0.0 0.00 1.0 1.00 3.0
GarageYrBlt 1379.0 1978.506164 24.689725 1900.0 1961.00 1980.0 2002.00 2010.0
GarageCars 1460.0 1.767123 0.747315 0.0 1.00 2.0 2.00 4.0
GarageArea 1460.0 472.980137 213.804841 0.0 334.50 480.0 576.00 1418.0
WoodDeckSF 1460.0 94.244521 125.338794 0.0 0.00 0.0 168.00 857.0
OpenPorchSF 1460.0 46.660274 66.256028 0.0 0.00 25.0 68.00 547.0
EnclosedPorch 1460.0 21.954110 61.119149 0.0 0.00 0.0 0.00 552.0
3SsnPorch 1460.0 3.409589 29.317331 0.0 0.00 0.0 0.00 508.0
ScreenPorch 1460.0 15.060959 55.757415 0.0 0.00 0.0 0.00 480.0
PoolArea 1460.0 2.758904 40.177307 0.0 0.00 0.0 0.00 738.0
MiscVal 1460.0 43.489041 496.123024 0.0 0.00 0.0 0.00 15500.0
MoSold 1460.0 6.321918 2.703626 1.0 5.00 6.0 8.00 12.0
YrSold 1460.0 2007.815753 1.328095 2006.0 2007.00 2008.0 2009.00 2010.0
SalePrice 1460.0 180921.195890 79442.502883 34900.0 129975.00 163000.0 214000.00 755000.0

First, I'd like to check the distribution of Lot Area. The max is much higher than the upper quartile.

In [8]:
plt.subplots(figsize = (16, 8));
sns.scatterplot(x = 'LotArea',y='SalePrice',data=train).set_title("Lot Area vs Sale Price",size=16);

I imagine the properties with the largest lot areas are farms with lots of land. The largest Lot Area is the test set is 56600. I choose to drop properties from the train set with a lot area above this.

In [9]:
test['LotArea'].max() # 56600
Out[9]:
56600
In [10]:
train = train[train['LotArea']<56600]
print('Remaining Properties in Training Set:',train.shape[0])
Remaining Properties in Training Set: 1453

Next, I'd like to check the Ground Living Area, again the max is far higher than the upper quartile.

In [11]:
plt.subplots(figsize = (16, 8));
sns.scatterplot(x = 'GrLivArea',y='SalePrice',data=train).set_title("Ground Floor Living Area vs Sale Price",size=16);

There appears to be a fairly strong linear relation, except for the point in the bottom right corner. I declare this an outlier and drop it from my test set.

In [12]:
train[['GrLivArea','SalePrice']].sort_values('GrLivArea',ascending=False).head(1) # The Outlier!
Out[12]:
GrLivArea SalePrice
523 4676 184750
In [13]:
train = train[(train['GrLivArea'] < 4600)]
print('Remaining Properties in Training Set:',train.shape[0])
Remaining Properties in Training Set: 1452

I am happy to move on to the next step, though there may be further outliers to remove when working on improving the models.

2. Check for skew and transform target variable (House Price) to have Normal Distribution.

This shouldn't actually be necessary thanks to the Central Limit Theorem. One to check if this has any impact on model accuracy.

In [14]:
plt.subplots(figsize = (16, 8));
sns.distplot(train['SalePrice']).set_title("Distribution of House Sale Prices",size=16);
In [15]:
plt.subplots(figsize = (16, 3));
fig = sns.boxplot(train['SalePrice']).set_title('Boxplot of House Sale Prices',size=16);
In [16]:
print("Skewness in SalePrice :", train['SalePrice'].skew())
print("Kurtosis in SalePrice :", train['SalePrice'].kurt())
Skewness in SalePrice : 1.8991383834139053
Kurtosis in SalePrice : 6.642615528379048

Apply a log transform to reduce right skew.

In [17]:
train['LogSalePrice'] = np.log(train['SalePrice']) # +1 if sale price < 1, else log is negative!
In [18]:
plt.subplots(figsize = (16, 8));
sns.distplot(train['LogSalePrice']).set_title("Distribution of Log-Transformed House Sale Prices",size=16);
In [19]:
print("Skewness in SalePrice :", train['LogSalePrice'].skew())
print("Kurtosis in SalePrice :", train['LogSalePrice'].kurt())
Skewness in SalePrice : 0.12530938026189326
Kurtosis in SalePrice : 0.826278184626108

3. Concatenate Train and Test sets to create a single frame to clean.

Note that this is the easiest and quickest way to ensure that my train and test sets have the same features after cleaning.

In [20]:
split_row = len(train)
y_train = train['LogSalePrice']
data = pd.concat([train, test],ignore_index=True, sort=False)
data
Out[20]:
Id MSSubClass MSZoning LotFrontage LotArea Street Alley LotShape LandContour Utilities LotConfig LandSlope Neighborhood Condition1 Condition2 BldgType HouseStyle OverallQual OverallCond YearBuilt YearRemodAdd RoofStyle RoofMatl Exterior1st Exterior2nd MasVnrType MasVnrArea ExterQual ExterCond Foundation BsmtQual BsmtCond BsmtExposure BsmtFinType1 BsmtFinSF1 BsmtFinType2 BsmtFinSF2 BsmtUnfSF TotalBsmtSF Heating HeatingQC CentralAir Electrical 1stFlrSF 2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath HalfBath BedroomAbvGr KitchenAbvGr KitchenQual TotRmsAbvGrd Functional Fireplaces FireplaceQu GarageType GarageYrBlt GarageFinish GarageCars GarageArea GarageQual GarageCond PavedDrive WoodDeckSF OpenPorchSF EnclosedPorch 3SsnPorch ScreenPorch PoolArea PoolQC Fence MiscFeature MiscVal MoSold YrSold SaleType SaleCondition SalePrice LogSalePrice
0 1 60 RL 65.0 8450 Pave NaN Reg Lvl AllPub Inside Gtl CollgCr Norm Norm 1Fam 2Story 7 5 2003 2003 Gable CompShg VinylSd VinylSd BrkFace 196.0 Gd TA PConc Gd TA No GLQ 706.0 Unf 0.0 150.0 856.0 GasA Ex Y SBrkr 856 854 0 1710 1.0 0.0 2 1 3 1 Gd 8 Typ 0 NaN Attchd 2003.0 RFn 2.0 548.0 TA TA Y 0 61 0 0 0 0 NaN NaN NaN 0 2 2008 WD Normal 208500.0 12.247694
1 2 20 RL 80.0 9600 Pave NaN Reg Lvl AllPub FR2 Gtl Veenker Feedr Norm 1Fam 1Story 6 8 1976 1976 Gable CompShg MetalSd MetalSd None 0.0 TA TA CBlock Gd TA Gd ALQ 978.0 Unf 0.0 284.0 1262.0 GasA Ex Y SBrkr 1262 0 0 1262 0.0 1.0 2 0 3 1 TA 6 Typ 1 TA Attchd 1976.0 RFn 2.0 460.0 TA TA Y 298 0 0 0 0 0 NaN NaN NaN 0 5 2007 WD Normal 181500.0 12.109011
2 3 60 RL 68.0 11250 Pave NaN IR1 Lvl AllPub Inside Gtl CollgCr Norm Norm 1Fam 2Story 7 5 2001 2002 Gable CompShg VinylSd VinylSd BrkFace 162.0 Gd TA PConc Gd TA Mn GLQ 486.0 Unf 0.0 434.0 920.0 GasA Ex Y SBrkr 920 866 0 1786 1.0 0.0 2 1 3 1 Gd 6 Typ 1 TA Attchd 2001.0 RFn 2.0 608.0 TA TA Y 0 42 0 0 0 0 NaN NaN NaN 0 9 2008 WD Normal 223500.0 12.317167
3 4 70 RL 60.0 9550 Pave NaN IR1 Lvl AllPub Corner Gtl Crawfor Norm Norm 1Fam 2Story 7 5 1915 1970 Gable CompShg Wd Sdng Wd Shng None 0.0 TA TA BrkTil TA Gd No ALQ 216.0 Unf 0.0 540.0 756.0 GasA Gd Y SBrkr 961 756 0 1717 1.0 0.0 1 0 3 1 Gd 7 Typ 1 Gd Detchd 1998.0 Unf 3.0 642.0 TA TA Y 0 35 272 0 0 0 NaN NaN NaN 0 2 2006 WD Abnorml 140000.0 11.849398
4 5 60 RL 84.0 14260 Pave NaN IR1 Lvl AllPub FR2 Gtl NoRidge Norm Norm 1Fam 2Story 8 5 2000 2000 Gable CompShg VinylSd VinylSd BrkFace 350.0 Gd TA PConc Gd TA Av GLQ 655.0 Unf 0.0 490.0 1145.0 GasA Ex Y SBrkr 1145 1053 0 2198 1.0 0.0 2 1 4 1 Gd 9 Typ 1 TA Attchd 2000.0 RFn 3.0 836.0 TA TA Y 192 84 0 0 0 0 NaN NaN NaN 0 12 2008 WD Normal 250000.0 12.429216
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
2906 2915 160 RM 21.0 1936 Pave NaN Reg Lvl AllPub Inside Gtl MeadowV Norm Norm Twnhs 2Story 4 7 1970 1970 Gable CompShg CemntBd CmentBd None 0.0 TA TA CBlock TA TA No Unf 0.0 Unf 0.0 546.0 546.0 GasA Gd Y SBrkr 546 546 0 1092 0.0 0.0 1 1 3 1 TA 5 Typ 0 NaN NaN NaN NaN 0.0 0.0 NaN NaN Y 0 0 0 0 0 0 NaN NaN NaN 0 6 2006 WD Normal NaN NaN
2907 2916 160 RM 21.0 1894 Pave NaN Reg Lvl AllPub Inside Gtl MeadowV Norm Norm TwnhsE 2Story 4 5 1970 1970 Gable CompShg CemntBd CmentBd None 0.0 TA TA CBlock TA TA No Rec 252.0 Unf 0.0 294.0 546.0 GasA TA Y SBrkr 546 546 0 1092 0.0 0.0 1 1 3 1 TA 6 Typ 0 NaN CarPort 1970.0 Unf 1.0 286.0 TA TA Y 0 24 0 0 0 0 NaN NaN NaN 0 4 2006 WD Abnorml NaN NaN
2908 2917 20 RL 160.0 20000 Pave NaN Reg Lvl AllPub Inside Gtl Mitchel Norm Norm 1Fam 1Story 5 7 1960 1996 Gable CompShg VinylSd VinylSd None 0.0 TA TA CBlock TA TA No ALQ 1224.0 Unf 0.0 0.0 1224.0 GasA Ex Y SBrkr 1224 0 0 1224 1.0 0.0 1 0 4 1 TA 7 Typ 1 TA Detchd 1960.0 Unf 2.0 576.0 TA TA Y 474 0 0 0 0 0 NaN NaN NaN 0 9 2006 WD Abnorml NaN NaN
2909 2918 85 RL 62.0 10441 Pave NaN Reg Lvl AllPub Inside Gtl Mitchel Norm Norm 1Fam SFoyer 5 5 1992 1992 Gable CompShg HdBoard Wd Shng None 0.0 TA TA PConc Gd TA Av GLQ 337.0 Unf 0.0 575.0 912.0 GasA TA Y SBrkr 970 0 0 970 0.0 1.0 1 0 3 1 TA 6 Typ 0 NaN NaN NaN NaN 0.0 0.0 NaN NaN Y 80 32 0 0 0 0 NaN MnPrv Shed 700 7 2006 WD Normal NaN NaN
2910 2919 60 RL 74.0 9627 Pave NaN Reg Lvl AllPub Inside Mod Mitchel Norm Norm 1Fam 2Story 7 5 1993 1994 Gable CompShg HdBoard HdBoard BrkFace 94.0 TA TA PConc Gd TA Av LwQ 758.0 Unf 0.0 238.0 996.0 GasA Ex Y SBrkr 996 1004 0 2000 0.0 0.0 2 1 3 1 TA 9 Typ 1 TA Attchd 1993.0 Fin 3.0 650.0 TA TA Y 190 48 0 0 0 0 NaN NaN NaN 0 11 2006 WD Normal NaN NaN

2911 rows × 82 columns

Dropping the target and Id columns.

In [21]:
data.drop(['SalePrice','LogSalePrice'],axis=1,inplace=True) #'Id'

4. Handle missing values through dropping columns or data imputation as appropriate.

First, a visual, with the null values in green. We see the features Alley, Fireplace Quality, Pool, Fence and Misc Feature each have lots of missing values.

In [22]:
plt.subplots(figsize = (16, 8));
sns.heatmap(data.isnull(), yticklabels = False, cbar = False, cmap ='Greens');
In [23]:
missing = pd.DataFrame(data.isnull().sum().reset_index()).rename({'index':'Feature',0:'Missing Value Count'},axis=1)
missing['Missing Value %'] = missing['Missing Value Count'] / len(data)
missing.sort_values('Missing Value %',ascending=False).head(34)
Out[23]:
Feature Missing Value Count Missing Value %
72 PoolQC 2902 0.996908
74 MiscFeature 2808 0.964617
6 Alley 2713 0.931982
73 Fence 2340 0.803847
57 FireplaceQu 1420 0.487805
3 LotFrontage 482 0.165579
59 GarageYrBlt 159 0.054620
60 GarageFinish 159 0.054620
63 GarageQual 159 0.054620
64 GarageCond 159 0.054620
58 GarageType 157 0.053933
32 BsmtExposure 82 0.028169
31 BsmtCond 82 0.028169
30 BsmtQual 81 0.027825
35 BsmtFinType2 80 0.027482
33 BsmtFinType1 79 0.027138
25 MasVnrType 24 0.008245
26 MasVnrArea 23 0.007901
2 MSZoning 4 0.001374
55 Functional 2 0.000687
48 BsmtHalfBath 2 0.000687
47 BsmtFullBath 2 0.000687
9 Utilities 2 0.000687
61 GarageCars 1 0.000344
53 KitchenQual 1 0.000344
34 BsmtFinSF1 1 0.000344
78 SaleType 1 0.000344
36 BsmtFinSF2 1 0.000344
37 BsmtUnfSF 1 0.000344
38 TotalBsmtSF 1 0.000344
24 Exterior2nd 1 0.000344
23 Exterior1st 1 0.000344
62 GarageArea 1 0.000344
42 Electrical 1 0.000344

This next part will be a bit of a slog. The aim is to tackle all 34 of the features with missing values, so that I have a complete dataset.

First, check the documentation which describes the features in the dataset. Notice that some features are null if the property does not have this feature. Pool and Garage are two examples. I will fill the null values with 'None'.

In [24]:
fill_with_none = ['PoolQC', 'MiscFeature', 'Alley', 'Fence', 'FireplaceQu', 'GarageCond',
       'GarageQual', 'GarageFinish', 'GarageType', 'BsmtCond', 'BsmtExposure',
       'BsmtQual', 'BsmtFinType2', 'BsmtFinType1', 'MasVnrType']

for column in fill_with_none:
    data[column].fillna('None',inplace =True)

Next, I choose to fill categorical variables with the modal value.

In [25]:
fill_with_mode = ['MSZoning','Functional', 'Utilities', 'Electrical', 'KitchenQual', 'SaleType',
       'Exterior2nd', 'Exterior1st']

for column in fill_with_mode:
    data[column].fillna(data[column].mode()[0],inplace=True)

Now, I choose to fill continuous variables with the median value.

Lot Frontage is an interesting one. There are enough missing values that could make it worthwhile exploring this further. One can imagine that this is function of LotArea, LotShape and LotConfig. Instead of imputing with the median, I could run regression of the named variables to predict the LotFrontage values for these 400 + properties.

This may be worth looking at when improving the model.

In [26]:
fill_with_median = ['GarageYrBlt', 'GarageCars', 'GarageArea', 'LotFrontage']

for column in fill_with_median:
    data[column].fillna(statistics.median(data[column]),inplace=True)

What's left?

In [27]:
missing = pd.DataFrame(data.isnull().sum().reset_index()).rename({'index':'Feature',0:'Missing Value Count'},axis=1)
missing['Missing Value %'] = missing['Missing Value Count'] / len(data)
missing[missing['Missing Value %']>0].sort_values('Missing Value %', ascending=False)
#list(missing[missing['Missing Value %']>0]['Feature'])
Out[27]:
Feature Missing Value Count Missing Value %
26 MasVnrArea 23 0.007901
47 BsmtFullBath 2 0.000687
48 BsmtHalfBath 2 0.000687
34 BsmtFinSF1 1 0.000344
36 BsmtFinSF2 1 0.000344
37 BsmtUnfSF 1 0.000344
38 TotalBsmtSF 1 0.000344

I choose to fill missing values from the remaining features with 0, based on their absence of Basement or Masonry Fireplace.

In [28]:
fill_with_0 = ['BsmtFinSF1', 'BsmtFinSF2', 'BsmtUnfSF', 'TotalBsmtSF', 'BsmtFullBath','BsmtHalfBath','MasVnrArea']

for column in fill_with_0:
    data[column].fillna(0,inplace=True)

What's left? Nothing, I have handled them all.

In [29]:
plt.subplots(figsize = (16, 8));
sns.heatmap(data.isnull(), yticklabels = False, cbar = False, cmap ='Greens');
In [30]:
missing = pd.DataFrame(data.isnull().sum().reset_index()).rename({'index':'Feature',0:'Missing Value Count'},axis=1)
missing['Missing Value %'] = missing['Missing Value Count'] / len(data)
missing[missing['Missing Value %']>0].sort_values('Missing Value %', ascending=False)
Out[30]:
Feature Missing Value Count Missing Value %

All Green -> No Null Values

5. Check for correlation between independent variables and remove any with high (> 0.9) collinearity.

In [31]:
f, ax = plt.subplots(figsize=(14, 10))
sns.heatmap(data.corr().abs(), 
        mask=np.triu(np.ones_like(data.corr().abs(), dtype=np.bool)),
        square=True, 
        linewidths=.1,
        center = 0.5,
        cmap='RdYlGn_r').set_title('Heatmap of All Features',size=16);
In [32]:
# Select upper triangle of correlation matrix
upper = data.corr().abs().where(np.triu(np.ones(data.corr().shape), k=1).astype(np.bool))

# Find index of feature columns with correlation greater than 0.9
to_drop = [column for column in upper.columns if any(upper[column] > 0.9)]

print('Drop Columns:',to_drop)


# Drop features 
data.drop(data[to_drop], axis=1,inplace=True)
Drop Columns: []

One might expect Year Built and Garage Year Built to exhibit stronger correlation. I'd like to take a look at the distributions of these.

In [33]:
plt.subplots(figsize = (16, 8));
sns.distplot(data['YearBuilt']).set_title("Distribution of House Year Built",size=16);
In [34]:
plt.subplots(figsize = (16, 3));
fig = sns.boxplot(data['YearBuilt']).set_title('Boxplot of House Year Built',size=16);
In [35]:
plt.subplots(figsize = (16, 8));
sns.distplot(data['GarageYrBlt']).set_title("Distribution of Garage Year Built",size=16);
In [36]:
sns.boxplot(data['GarageYrBlt']).set_title("Distribution of Garage Year Built",size=16);

Aha, an outlier! Clearly the garage was built in 2007 instead of 2207!

In [37]:
data.at[2584, 'GarageYrBlt'] = 2007 # Setting this value in the dataframe.

6. Consider binning categorical variables to create more helpful features.

E.g. Overall Quality could be Great, Okay or Poor to cut down 10 features to 3.

I choose not to do this now, and leave this as something which could further improve later models.

7. Apply one-hot encoding on categorical variables.

First transform numeric variables into categorical variables if their numerical value doesn't matter. For example, the month of sale is encoded between 1 and 12, but it doesn't make sense for the model to consider this.

In [38]:
change_to_string = ['MSSubClass','YearBuilt', 'YearRemodAdd','GarageYrBlt','MoSold','YrSold']

for column in change_to_string:
    data[column] = data[column].apply(str)
In [39]:
data = pd.get_dummies(data,drop_first=True) # Drop First = True removes issues with linear dependence later on.
In [40]:
data
Out[40]:
Id LotFrontage LotArea OverallQual OverallCond MasVnrArea BsmtFinSF1 BsmtFinSF2 BsmtUnfSF TotalBsmtSF 1stFlrSF 2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath HalfBath BedroomAbvGr KitchenAbvGr TotRmsAbvGrd Fireplaces GarageCars GarageArea WoodDeckSF OpenPorchSF EnclosedPorch 3SsnPorch ScreenPorch PoolArea MiscVal MSSubClass_150 MSSubClass_160 MSSubClass_180 MSSubClass_190 MSSubClass_20 MSSubClass_30 MSSubClass_40 MSSubClass_45 MSSubClass_50 MSSubClass_60 MSSubClass_70 MSSubClass_75 MSSubClass_80 MSSubClass_85 MSSubClass_90 MSZoning_FV MSZoning_RH MSZoning_RL MSZoning_RM Street_Pave Alley_None Alley_Pave LotShape_IR2 LotShape_IR3 LotShape_Reg LandContour_HLS LandContour_Low LandContour_Lvl Utilities_NoSeWa LotConfig_CulDSac LotConfig_FR2 LotConfig_FR3 LotConfig_Inside LandSlope_Mod LandSlope_Sev Neighborhood_Blueste Neighborhood_BrDale Neighborhood_BrkSide Neighborhood_ClearCr Neighborhood_CollgCr Neighborhood_Crawfor Neighborhood_Edwards Neighborhood_Gilbert Neighborhood_IDOTRR Neighborhood_MeadowV Neighborhood_Mitchel Neighborhood_NAmes Neighborhood_NPkVill Neighborhood_NWAmes Neighborhood_NoRidge Neighborhood_NridgHt Neighborhood_OldTown Neighborhood_SWISU Neighborhood_Sawyer Neighborhood_SawyerW Neighborhood_Somerst Neighborhood_StoneBr Neighborhood_Timber Neighborhood_Veenker Condition1_Feedr Condition1_Norm Condition1_PosA Condition1_PosN Condition1_RRAe Condition1_RRAn Condition1_RRNe Condition1_RRNn Condition2_Feedr Condition2_Norm Condition2_PosA Condition2_PosN Condition2_RRAe Condition2_RRAn Condition2_RRNn BldgType_2fmCon BldgType_Duplex BldgType_Twnhs BldgType_TwnhsE HouseStyle_1.5Unf HouseStyle_1Story HouseStyle_2.5Fin HouseStyle_2.5Unf HouseStyle_2Story HouseStyle_SFoyer HouseStyle_SLvl YearBuilt_1875 YearBuilt_1879 YearBuilt_1880 YearBuilt_1882 YearBuilt_1885 YearBuilt_1890 YearBuilt_1892 YearBuilt_1893 YearBuilt_1895 YearBuilt_1896 YearBuilt_1898 YearBuilt_1900 YearBuilt_1901 YearBuilt_1902 YearBuilt_1904 YearBuilt_1905 YearBuilt_1906 YearBuilt_1907 YearBuilt_1908 YearBuilt_1910 YearBuilt_1911 YearBuilt_1912 YearBuilt_1913 YearBuilt_1914 YearBuilt_1915 YearBuilt_1916 YearBuilt_1917 YearBuilt_1918 YearBuilt_1919 YearBuilt_1920 YearBuilt_1921 YearBuilt_1922 YearBuilt_1923 YearBuilt_1924 YearBuilt_1925 YearBuilt_1926 YearBuilt_1927 YearBuilt_1928 YearBuilt_1929 YearBuilt_1930 YearBuilt_1931 YearBuilt_1932 YearBuilt_1934 YearBuilt_1935 YearBuilt_1936 YearBuilt_1937 YearBuilt_1938 YearBuilt_1939 YearBuilt_1940 YearBuilt_1941 YearBuilt_1942 YearBuilt_1945 YearBuilt_1946 YearBuilt_1947 YearBuilt_1948 YearBuilt_1949 YearBuilt_1950 YearBuilt_1951 YearBuilt_1952 YearBuilt_1953 YearBuilt_1954 YearBuilt_1955 YearBuilt_1956 YearBuilt_1957 YearBuilt_1958 YearBuilt_1959 YearBuilt_1960 YearBuilt_1961 YearBuilt_1962 YearBuilt_1963 YearBuilt_1964 YearBuilt_1965 YearBuilt_1966 YearBuilt_1967 YearBuilt_1968 YearBuilt_1969 YearBuilt_1970 YearBuilt_1971 YearBuilt_1972 YearBuilt_1973 YearBuilt_1974 YearBuilt_1975 YearBuilt_1976 YearBuilt_1977 YearBuilt_1978 YearBuilt_1979 YearBuilt_1980 YearBuilt_1981 YearBuilt_1982 YearBuilt_1983 YearBuilt_1984 YearBuilt_1985 YearBuilt_1986 YearBuilt_1987 YearBuilt_1988 YearBuilt_1989 YearBuilt_1990 YearBuilt_1991 YearBuilt_1992 YearBuilt_1993 YearBuilt_1994 YearBuilt_1995 YearBuilt_1996 YearBuilt_1997 YearBuilt_1998 YearBuilt_1999 YearBuilt_2000 YearBuilt_2001 YearBuilt_2002 YearBuilt_2003 YearBuilt_2004 YearBuilt_2005 YearBuilt_2006 YearBuilt_2007 YearBuilt_2008 YearBuilt_2009 YearBuilt_2010 YearRemodAdd_1951 YearRemodAdd_1952 YearRemodAdd_1953 YearRemodAdd_1954 YearRemodAdd_1955 YearRemodAdd_1956 YearRemodAdd_1957 YearRemodAdd_1958 YearRemodAdd_1959 YearRemodAdd_1960 YearRemodAdd_1961 YearRemodAdd_1962 YearRemodAdd_1963 YearRemodAdd_1964 YearRemodAdd_1965 YearRemodAdd_1966 YearRemodAdd_1967 YearRemodAdd_1968 YearRemodAdd_1969 YearRemodAdd_1970 YearRemodAdd_1971 YearRemodAdd_1972 YearRemodAdd_1973 YearRemodAdd_1974 YearRemodAdd_1975 YearRemodAdd_1976 YearRemodAdd_1977 YearRemodAdd_1978 YearRemodAdd_1979 YearRemodAdd_1980 YearRemodAdd_1981 YearRemodAdd_1982 YearRemodAdd_1983 YearRemodAdd_1984 YearRemodAdd_1985 YearRemodAdd_1986 YearRemodAdd_1987 YearRemodAdd_1988 YearRemodAdd_1989 YearRemodAdd_1990 YearRemodAdd_1991 YearRemodAdd_1992 YearRemodAdd_1993 YearRemodAdd_1994 YearRemodAdd_1995 YearRemodAdd_1996 YearRemodAdd_1997 YearRemodAdd_1998 YearRemodAdd_1999 YearRemodAdd_2000 YearRemodAdd_2001 YearRemodAdd_2002 YearRemodAdd_2003 YearRemodAdd_2004 YearRemodAdd_2005 YearRemodAdd_2006 YearRemodAdd_2007 YearRemodAdd_2008 YearRemodAdd_2009 YearRemodAdd_2010 RoofStyle_Gable RoofStyle_Gambrel RoofStyle_Hip RoofStyle_Mansard RoofStyle_Shed RoofMatl_Membran RoofMatl_Metal RoofMatl_Roll RoofMatl_Tar&Grv RoofMatl_WdShake RoofMatl_WdShngl Exterior1st_AsphShn Exterior1st_BrkComm Exterior1st_BrkFace Exterior1st_CBlock Exterior1st_CemntBd Exterior1st_HdBoard Exterior1st_ImStucc Exterior1st_MetalSd Exterior1st_Plywood Exterior1st_Stone Exterior1st_Stucco Exterior1st_VinylSd Exterior1st_Wd Sdng Exterior1st_WdShing Exterior2nd_AsphShn Exterior2nd_Brk Cmn Exterior2nd_BrkFace Exterior2nd_CBlock Exterior2nd_CmentBd Exterior2nd_HdBoard Exterior2nd_ImStucc Exterior2nd_MetalSd Exterior2nd_Other Exterior2nd_Plywood Exterior2nd_Stone Exterior2nd_Stucco Exterior2nd_VinylSd Exterior2nd_Wd Sdng Exterior2nd_Wd Shng MasVnrType_BrkFace MasVnrType_None MasVnrType_Stone ExterQual_Fa ExterQual_Gd ExterQual_TA ExterCond_Fa ExterCond_Gd ExterCond_Po ExterCond_TA Foundation_CBlock Foundation_PConc Foundation_Slab Foundation_Stone Foundation_Wood BsmtQual_Fa BsmtQual_Gd BsmtQual_None BsmtQual_TA BsmtCond_Gd BsmtCond_None BsmtCond_Po BsmtCond_TA BsmtExposure_Gd BsmtExposure_Mn BsmtExposure_No BsmtExposure_None BsmtFinType1_BLQ BsmtFinType1_GLQ BsmtFinType1_LwQ BsmtFinType1_None BsmtFinType1_Rec BsmtFinType1_Unf BsmtFinType2_BLQ BsmtFinType2_GLQ BsmtFinType2_LwQ BsmtFinType2_None BsmtFinType2_Rec BsmtFinType2_Unf Heating_GasA Heating_GasW Heating_Grav Heating_OthW Heating_Wall HeatingQC_Fa HeatingQC_Gd HeatingQC_Po HeatingQC_TA CentralAir_Y Electrical_FuseF Electrical_FuseP Electrical_Mix Electrical_SBrkr KitchenQual_Fa KitchenQual_Gd KitchenQual_TA Functional_Maj2 Functional_Min1 Functional_Min2 Functional_Mod Functional_Sev Functional_Typ FireplaceQu_Fa FireplaceQu_Gd FireplaceQu_None FireplaceQu_Po FireplaceQu_TA GarageType_Attchd GarageType_Basment GarageType_BuiltIn GarageType_CarPort GarageType_Detchd GarageType_None GarageYrBlt_1896.0 GarageYrBlt_1900.0 GarageYrBlt_1906.0 GarageYrBlt_1908.0 GarageYrBlt_1910.0 GarageYrBlt_1914.0 GarageYrBlt_1915.0 GarageYrBlt_1916.0 GarageYrBlt_1917.0 GarageYrBlt_1918.0 GarageYrBlt_1919.0 GarageYrBlt_1920.0 GarageYrBlt_1921.0 GarageYrBlt_1922.0 GarageYrBlt_1923.0 GarageYrBlt_1924.0 GarageYrBlt_1925.0 GarageYrBlt_1926.0 GarageYrBlt_1927.0 GarageYrBlt_1928.0 GarageYrBlt_1929.0 GarageYrBlt_1930.0 GarageYrBlt_1931.0 GarageYrBlt_1932.0 GarageYrBlt_1933.0 GarageYrBlt_1934.0 GarageYrBlt_1935.0 GarageYrBlt_1936.0 GarageYrBlt_1937.0 GarageYrBlt_1938.0 GarageYrBlt_1939.0 GarageYrBlt_1940.0 GarageYrBlt_1941.0 GarageYrBlt_1942.0 GarageYrBlt_1943.0 GarageYrBlt_1945.0 GarageYrBlt_1946.0 GarageYrBlt_1947.0 GarageYrBlt_1948.0 GarageYrBlt_1949.0 GarageYrBlt_1950.0 GarageYrBlt_1951.0 GarageYrBlt_1952.0 GarageYrBlt_1953.0 GarageYrBlt_1954.0 GarageYrBlt_1955.0 GarageYrBlt_1956.0 GarageYrBlt_1957.0 GarageYrBlt_1958.0 GarageYrBlt_1959.0 GarageYrBlt_1960.0 GarageYrBlt_1961.0 GarageYrBlt_1962.0 GarageYrBlt_1963.0 GarageYrBlt_1964.0 GarageYrBlt_1965.0 GarageYrBlt_1966.0 GarageYrBlt_1967.0 GarageYrBlt_1968.0 GarageYrBlt_1969.0 GarageYrBlt_1970.0 GarageYrBlt_1971.0 GarageYrBlt_1972.0 GarageYrBlt_1973.0 GarageYrBlt_1974.0 GarageYrBlt_1975.0 GarageYrBlt_1976.0 GarageYrBlt_1977.0 GarageYrBlt_1978.0 GarageYrBlt_1979.0 GarageYrBlt_1980.0 GarageYrBlt_1981.0 GarageYrBlt_1982.0 GarageYrBlt_1983.0 GarageYrBlt_1984.0 GarageYrBlt_1985.0 GarageYrBlt_1986.0 GarageYrBlt_1987.0 GarageYrBlt_1988.0 GarageYrBlt_1989.0 GarageYrBlt_1990.0 GarageYrBlt_1991.0 GarageYrBlt_1992.0 GarageYrBlt_1993.0 GarageYrBlt_1994.0 GarageYrBlt_1995.0 GarageYrBlt_1996.0 GarageYrBlt_1997.0 GarageYrBlt_1998.0 GarageYrBlt_1999.0 GarageYrBlt_2000.0 GarageYrBlt_2001.0 GarageYrBlt_2002.0 GarageYrBlt_2003.0 GarageYrBlt_2004.0 GarageYrBlt_2005.0 GarageYrBlt_2006.0 GarageYrBlt_2007.0 GarageYrBlt_2008.0 GarageYrBlt_2009.0 GarageYrBlt_2010.0 GarageFinish_None GarageFinish_RFn GarageFinish_Unf GarageQual_Fa GarageQual_Gd GarageQual_None GarageQual_Po GarageQual_TA GarageCond_Fa GarageCond_Gd GarageCond_None GarageCond_Po GarageCond_TA PavedDrive_P PavedDrive_Y PoolQC_Fa PoolQC_Gd PoolQC_None Fence_GdWo Fence_MnPrv Fence_MnWw Fence_None MiscFeature_None MiscFeature_Othr MiscFeature_Shed MiscFeature_TenC MoSold_10 MoSold_11 MoSold_12 MoSold_2 MoSold_3 MoSold_4 MoSold_5 MoSold_6 MoSold_7 MoSold_8 MoSold_9 YrSold_2007 YrSold_2008 YrSold_2009 YrSold_2010 SaleType_CWD SaleType_Con SaleType_ConLD SaleType_ConLI SaleType_ConLw SaleType_New SaleType_Oth SaleType_WD SaleCondition_AdjLand SaleCondition_Alloca SaleCondition_Family SaleCondition_Normal SaleCondition_Partial
0 1 65.0 8450 7 5 196.0 706.0 0.0 150.0 856.0 856 854 0 1710 1.0 0.0 2 1 3 1 8 0 2.0 548.0 0 61 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0
1 2 80.0 9600 6 8 0.0 978.0 0.0 284.0 1262.0 1262 0 0 1262 0.0 1.0 2 0 3 1 6 1 2.0 460.0 298 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0
2 3 68.0 11250 7 5 162.0 486.0 0.0 434.0 920.0 920 866 0 1786 1.0 0.0 2 1 3 1 6 1 2.0 608.0 0 42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0
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4 5 84.0 14260 8 5 350.0 655.0 0.0 490.0 1145.0 1145 1053 0 2198 1.0 0.0 2 1 4 1 9 1 3.0 836.0 192 84 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
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2911 rows × 561 columns

8. Split clean frame back into train and test splits.

In [41]:
train = data[:split_row]  #Recall that we set split_row = len(train) when concatenating
test = data[split_row:]
train
test
Out[41]:
Id LotFrontage LotArea OverallQual OverallCond MasVnrArea BsmtFinSF1 BsmtFinSF2 BsmtUnfSF TotalBsmtSF 1stFlrSF 2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath HalfBath BedroomAbvGr KitchenAbvGr TotRmsAbvGrd Fireplaces GarageCars GarageArea WoodDeckSF OpenPorchSF EnclosedPorch 3SsnPorch ScreenPorch PoolArea MiscVal MSSubClass_150 MSSubClass_160 MSSubClass_180 MSSubClass_190 MSSubClass_20 MSSubClass_30 MSSubClass_40 MSSubClass_45 MSSubClass_50 MSSubClass_60 MSSubClass_70 MSSubClass_75 MSSubClass_80 MSSubClass_85 MSSubClass_90 MSZoning_FV MSZoning_RH MSZoning_RL MSZoning_RM Street_Pave Alley_None Alley_Pave LotShape_IR2 LotShape_IR3 LotShape_Reg LandContour_HLS LandContour_Low LandContour_Lvl Utilities_NoSeWa LotConfig_CulDSac LotConfig_FR2 LotConfig_FR3 LotConfig_Inside LandSlope_Mod LandSlope_Sev Neighborhood_Blueste Neighborhood_BrDale Neighborhood_BrkSide Neighborhood_ClearCr Neighborhood_CollgCr Neighborhood_Crawfor Neighborhood_Edwards Neighborhood_Gilbert Neighborhood_IDOTRR Neighborhood_MeadowV Neighborhood_Mitchel Neighborhood_NAmes Neighborhood_NPkVill Neighborhood_NWAmes Neighborhood_NoRidge Neighborhood_NridgHt Neighborhood_OldTown Neighborhood_SWISU Neighborhood_Sawyer Neighborhood_SawyerW Neighborhood_Somerst Neighborhood_StoneBr Neighborhood_Timber Neighborhood_Veenker Condition1_Feedr Condition1_Norm Condition1_PosA Condition1_PosN Condition1_RRAe Condition1_RRAn Condition1_RRNe Condition1_RRNn Condition2_Feedr Condition2_Norm Condition2_PosA Condition2_PosN Condition2_RRAe Condition2_RRAn Condition2_RRNn BldgType_2fmCon BldgType_Duplex BldgType_Twnhs BldgType_TwnhsE HouseStyle_1.5Unf HouseStyle_1Story HouseStyle_2.5Fin HouseStyle_2.5Unf HouseStyle_2Story HouseStyle_SFoyer HouseStyle_SLvl YearBuilt_1875 YearBuilt_1879 YearBuilt_1880 YearBuilt_1882 YearBuilt_1885 YearBuilt_1890 YearBuilt_1892 YearBuilt_1893 YearBuilt_1895 YearBuilt_1896 YearBuilt_1898 YearBuilt_1900 YearBuilt_1901 YearBuilt_1902 YearBuilt_1904 YearBuilt_1905 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YearRemodAdd_1977 YearRemodAdd_1978 YearRemodAdd_1979 YearRemodAdd_1980 YearRemodAdd_1981 YearRemodAdd_1982 YearRemodAdd_1983 YearRemodAdd_1984 YearRemodAdd_1985 YearRemodAdd_1986 YearRemodAdd_1987 YearRemodAdd_1988 YearRemodAdd_1989 YearRemodAdd_1990 YearRemodAdd_1991 YearRemodAdd_1992 YearRemodAdd_1993 YearRemodAdd_1994 YearRemodAdd_1995 YearRemodAdd_1996 YearRemodAdd_1997 YearRemodAdd_1998 YearRemodAdd_1999 YearRemodAdd_2000 YearRemodAdd_2001 YearRemodAdd_2002 YearRemodAdd_2003 YearRemodAdd_2004 YearRemodAdd_2005 YearRemodAdd_2006 YearRemodAdd_2007 YearRemodAdd_2008 YearRemodAdd_2009 YearRemodAdd_2010 RoofStyle_Gable RoofStyle_Gambrel RoofStyle_Hip RoofStyle_Mansard RoofStyle_Shed RoofMatl_Membran RoofMatl_Metal RoofMatl_Roll RoofMatl_Tar&Grv RoofMatl_WdShake RoofMatl_WdShngl Exterior1st_AsphShn Exterior1st_BrkComm Exterior1st_BrkFace Exterior1st_CBlock Exterior1st_CemntBd Exterior1st_HdBoard Exterior1st_ImStucc Exterior1st_MetalSd Exterior1st_Plywood Exterior1st_Stone Exterior1st_Stucco Exterior1st_VinylSd Exterior1st_Wd Sdng Exterior1st_WdShing Exterior2nd_AsphShn Exterior2nd_Brk Cmn Exterior2nd_BrkFace Exterior2nd_CBlock Exterior2nd_CmentBd Exterior2nd_HdBoard Exterior2nd_ImStucc Exterior2nd_MetalSd Exterior2nd_Other Exterior2nd_Plywood Exterior2nd_Stone Exterior2nd_Stucco Exterior2nd_VinylSd Exterior2nd_Wd Sdng Exterior2nd_Wd Shng MasVnrType_BrkFace MasVnrType_None MasVnrType_Stone ExterQual_Fa ExterQual_Gd ExterQual_TA ExterCond_Fa ExterCond_Gd ExterCond_Po ExterCond_TA Foundation_CBlock Foundation_PConc Foundation_Slab Foundation_Stone Foundation_Wood BsmtQual_Fa BsmtQual_Gd BsmtQual_None BsmtQual_TA BsmtCond_Gd BsmtCond_None BsmtCond_Po BsmtCond_TA BsmtExposure_Gd BsmtExposure_Mn BsmtExposure_No BsmtExposure_None BsmtFinType1_BLQ BsmtFinType1_GLQ BsmtFinType1_LwQ BsmtFinType1_None BsmtFinType1_Rec BsmtFinType1_Unf BsmtFinType2_BLQ BsmtFinType2_GLQ BsmtFinType2_LwQ BsmtFinType2_None BsmtFinType2_Rec BsmtFinType2_Unf Heating_GasA Heating_GasW 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1452 rows × 561 columns

Out[41]:
Id LotFrontage LotArea OverallQual OverallCond MasVnrArea BsmtFinSF1 BsmtFinSF2 BsmtUnfSF TotalBsmtSF 1stFlrSF 2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath HalfBath BedroomAbvGr KitchenAbvGr TotRmsAbvGrd Fireplaces GarageCars GarageArea WoodDeckSF OpenPorchSF EnclosedPorch 3SsnPorch ScreenPorch PoolArea MiscVal MSSubClass_150 MSSubClass_160 MSSubClass_180 MSSubClass_190 MSSubClass_20 MSSubClass_30 MSSubClass_40 MSSubClass_45 MSSubClass_50 MSSubClass_60 MSSubClass_70 MSSubClass_75 MSSubClass_80 MSSubClass_85 MSSubClass_90 MSZoning_FV MSZoning_RH MSZoning_RL MSZoning_RM Street_Pave Alley_None Alley_Pave LotShape_IR2 LotShape_IR3 LotShape_Reg LandContour_HLS LandContour_Low LandContour_Lvl Utilities_NoSeWa LotConfig_CulDSac LotConfig_FR2 LotConfig_FR3 LotConfig_Inside LandSlope_Mod LandSlope_Sev Neighborhood_Blueste Neighborhood_BrDale Neighborhood_BrkSide Neighborhood_ClearCr Neighborhood_CollgCr Neighborhood_Crawfor Neighborhood_Edwards Neighborhood_Gilbert Neighborhood_IDOTRR Neighborhood_MeadowV Neighborhood_Mitchel Neighborhood_NAmes Neighborhood_NPkVill Neighborhood_NWAmes Neighborhood_NoRidge Neighborhood_NridgHt Neighborhood_OldTown Neighborhood_SWISU Neighborhood_Sawyer Neighborhood_SawyerW Neighborhood_Somerst Neighborhood_StoneBr Neighborhood_Timber Neighborhood_Veenker Condition1_Feedr Condition1_Norm Condition1_PosA Condition1_PosN Condition1_RRAe Condition1_RRAn Condition1_RRNe Condition1_RRNn Condition2_Feedr Condition2_Norm Condition2_PosA Condition2_PosN Condition2_RRAe Condition2_RRAn Condition2_RRNn BldgType_2fmCon BldgType_Duplex BldgType_Twnhs BldgType_TwnhsE HouseStyle_1.5Unf HouseStyle_1Story HouseStyle_2.5Fin HouseStyle_2.5Unf HouseStyle_2Story HouseStyle_SFoyer HouseStyle_SLvl YearBuilt_1875 YearBuilt_1879 YearBuilt_1880 YearBuilt_1882 YearBuilt_1885 YearBuilt_1890 YearBuilt_1892 YearBuilt_1893 YearBuilt_1895 YearBuilt_1896 YearBuilt_1898 YearBuilt_1900 YearBuilt_1901 YearBuilt_1902 YearBuilt_1904 YearBuilt_1905 YearBuilt_1906 YearBuilt_1907 YearBuilt_1908 YearBuilt_1910 YearBuilt_1911 YearBuilt_1912 YearBuilt_1913 YearBuilt_1914 YearBuilt_1915 YearBuilt_1916 YearBuilt_1917 YearBuilt_1918 YearBuilt_1919 YearBuilt_1920 YearBuilt_1921 YearBuilt_1922 YearBuilt_1923 YearBuilt_1924 YearBuilt_1925 YearBuilt_1926 YearBuilt_1927 YearBuilt_1928 YearBuilt_1929 YearBuilt_1930 YearBuilt_1931 YearBuilt_1932 YearBuilt_1934 YearBuilt_1935 YearBuilt_1936 YearBuilt_1937 YearBuilt_1938 YearBuilt_1939 YearBuilt_1940 YearBuilt_1941 YearBuilt_1942 YearBuilt_1945 YearBuilt_1946 YearBuilt_1947 YearBuilt_1948 YearBuilt_1949 YearBuilt_1950 YearBuilt_1951 YearBuilt_1952 YearBuilt_1953 YearBuilt_1954 YearBuilt_1955 YearBuilt_1956 YearBuilt_1957 YearBuilt_1958 YearBuilt_1959 YearBuilt_1960 YearBuilt_1961 YearBuilt_1962 YearBuilt_1963 YearBuilt_1964 YearBuilt_1965 YearBuilt_1966 YearBuilt_1967 YearBuilt_1968 YearBuilt_1969 YearBuilt_1970 YearBuilt_1971 YearBuilt_1972 YearBuilt_1973 YearBuilt_1974 YearBuilt_1975 YearBuilt_1976 YearBuilt_1977 YearBuilt_1978 YearBuilt_1979 YearBuilt_1980 YearBuilt_1981 YearBuilt_1982 YearBuilt_1983 YearBuilt_1984 YearBuilt_1985 YearBuilt_1986 YearBuilt_1987 YearBuilt_1988 YearBuilt_1989 YearBuilt_1990 YearBuilt_1991 YearBuilt_1992 YearBuilt_1993 YearBuilt_1994 YearBuilt_1995 YearBuilt_1996 YearBuilt_1997 YearBuilt_1998 YearBuilt_1999 YearBuilt_2000 YearBuilt_2001 YearBuilt_2002 YearBuilt_2003 YearBuilt_2004 YearBuilt_2005 YearBuilt_2006 YearBuilt_2007 YearBuilt_2008 YearBuilt_2009 YearBuilt_2010 YearRemodAdd_1951 YearRemodAdd_1952 YearRemodAdd_1953 YearRemodAdd_1954 YearRemodAdd_1955 YearRemodAdd_1956 YearRemodAdd_1957 YearRemodAdd_1958 YearRemodAdd_1959 YearRemodAdd_1960 YearRemodAdd_1961 YearRemodAdd_1962 YearRemodAdd_1963 YearRemodAdd_1964 YearRemodAdd_1965 YearRemodAdd_1966 YearRemodAdd_1967 YearRemodAdd_1968 YearRemodAdd_1969 YearRemodAdd_1970 YearRemodAdd_1971 YearRemodAdd_1972 YearRemodAdd_1973 YearRemodAdd_1974 YearRemodAdd_1975 YearRemodAdd_1976 YearRemodAdd_1977 YearRemodAdd_1978 YearRemodAdd_1979 YearRemodAdd_1980 YearRemodAdd_1981 YearRemodAdd_1982 YearRemodAdd_1983 YearRemodAdd_1984 YearRemodAdd_1985 YearRemodAdd_1986 YearRemodAdd_1987 YearRemodAdd_1988 YearRemodAdd_1989 YearRemodAdd_1990 YearRemodAdd_1991 YearRemodAdd_1992 YearRemodAdd_1993 YearRemodAdd_1994 YearRemodAdd_1995 YearRemodAdd_1996 YearRemodAdd_1997 YearRemodAdd_1998 YearRemodAdd_1999 YearRemodAdd_2000 YearRemodAdd_2001 YearRemodAdd_2002 YearRemodAdd_2003 YearRemodAdd_2004 YearRemodAdd_2005 YearRemodAdd_2006 YearRemodAdd_2007 YearRemodAdd_2008 YearRemodAdd_2009 YearRemodAdd_2010 RoofStyle_Gable RoofStyle_Gambrel RoofStyle_Hip RoofStyle_Mansard RoofStyle_Shed RoofMatl_Membran RoofMatl_Metal RoofMatl_Roll RoofMatl_Tar&Grv RoofMatl_WdShake RoofMatl_WdShngl Exterior1st_AsphShn Exterior1st_BrkComm Exterior1st_BrkFace Exterior1st_CBlock Exterior1st_CemntBd Exterior1st_HdBoard Exterior1st_ImStucc Exterior1st_MetalSd Exterior1st_Plywood Exterior1st_Stone Exterior1st_Stucco Exterior1st_VinylSd Exterior1st_Wd Sdng Exterior1st_WdShing Exterior2nd_AsphShn Exterior2nd_Brk Cmn Exterior2nd_BrkFace Exterior2nd_CBlock Exterior2nd_CmentBd Exterior2nd_HdBoard Exterior2nd_ImStucc Exterior2nd_MetalSd Exterior2nd_Other Exterior2nd_Plywood Exterior2nd_Stone Exterior2nd_Stucco Exterior2nd_VinylSd Exterior2nd_Wd Sdng Exterior2nd_Wd Shng MasVnrType_BrkFace MasVnrType_None MasVnrType_Stone ExterQual_Fa ExterQual_Gd ExterQual_TA ExterCond_Fa ExterCond_Gd ExterCond_Po ExterCond_TA Foundation_CBlock Foundation_PConc Foundation_Slab Foundation_Stone Foundation_Wood BsmtQual_Fa BsmtQual_Gd BsmtQual_None BsmtQual_TA BsmtCond_Gd BsmtCond_None BsmtCond_Po BsmtCond_TA BsmtExposure_Gd BsmtExposure_Mn BsmtExposure_No BsmtExposure_None BsmtFinType1_BLQ BsmtFinType1_GLQ BsmtFinType1_LwQ BsmtFinType1_None BsmtFinType1_Rec BsmtFinType1_Unf BsmtFinType2_BLQ BsmtFinType2_GLQ BsmtFinType2_LwQ BsmtFinType2_None BsmtFinType2_Rec BsmtFinType2_Unf Heating_GasA Heating_GasW Heating_Grav Heating_OthW Heating_Wall HeatingQC_Fa HeatingQC_Gd HeatingQC_Po HeatingQC_TA CentralAir_Y Electrical_FuseF Electrical_FuseP Electrical_Mix Electrical_SBrkr KitchenQual_Fa KitchenQual_Gd KitchenQual_TA Functional_Maj2 Functional_Min1 Functional_Min2 Functional_Mod Functional_Sev Functional_Typ FireplaceQu_Fa FireplaceQu_Gd FireplaceQu_None FireplaceQu_Po FireplaceQu_TA GarageType_Attchd GarageType_Basment GarageType_BuiltIn GarageType_CarPort GarageType_Detchd GarageType_None GarageYrBlt_1896.0 GarageYrBlt_1900.0 GarageYrBlt_1906.0 GarageYrBlt_1908.0 GarageYrBlt_1910.0 GarageYrBlt_1914.0 GarageYrBlt_1915.0 GarageYrBlt_1916.0 GarageYrBlt_1917.0 GarageYrBlt_1918.0 GarageYrBlt_1919.0 GarageYrBlt_1920.0 GarageYrBlt_1921.0 GarageYrBlt_1922.0 GarageYrBlt_1923.0 GarageYrBlt_1924.0 GarageYrBlt_1925.0 GarageYrBlt_1926.0 GarageYrBlt_1927.0 GarageYrBlt_1928.0 GarageYrBlt_1929.0 GarageYrBlt_1930.0 GarageYrBlt_1931.0 GarageYrBlt_1932.0 GarageYrBlt_1933.0 GarageYrBlt_1934.0 GarageYrBlt_1935.0 GarageYrBlt_1936.0 GarageYrBlt_1937.0 GarageYrBlt_1938.0 GarageYrBlt_1939.0 GarageYrBlt_1940.0 GarageYrBlt_1941.0 GarageYrBlt_1942.0 GarageYrBlt_1943.0 GarageYrBlt_1945.0 GarageYrBlt_1946.0 GarageYrBlt_1947.0 GarageYrBlt_1948.0 GarageYrBlt_1949.0 GarageYrBlt_1950.0 GarageYrBlt_1951.0 GarageYrBlt_1952.0 GarageYrBlt_1953.0 GarageYrBlt_1954.0 GarageYrBlt_1955.0 GarageYrBlt_1956.0 GarageYrBlt_1957.0 GarageYrBlt_1958.0 GarageYrBlt_1959.0 GarageYrBlt_1960.0 GarageYrBlt_1961.0 GarageYrBlt_1962.0 GarageYrBlt_1963.0 GarageYrBlt_1964.0 GarageYrBlt_1965.0 GarageYrBlt_1966.0 GarageYrBlt_1967.0 GarageYrBlt_1968.0 GarageYrBlt_1969.0 GarageYrBlt_1970.0 GarageYrBlt_1971.0 GarageYrBlt_1972.0 GarageYrBlt_1973.0 GarageYrBlt_1974.0 GarageYrBlt_1975.0 GarageYrBlt_1976.0 GarageYrBlt_1977.0 GarageYrBlt_1978.0 GarageYrBlt_1979.0 GarageYrBlt_1980.0 GarageYrBlt_1981.0 GarageYrBlt_1982.0 GarageYrBlt_1983.0 GarageYrBlt_1984.0 GarageYrBlt_1985.0 GarageYrBlt_1986.0 GarageYrBlt_1987.0 GarageYrBlt_1988.0 GarageYrBlt_1989.0 GarageYrBlt_1990.0 GarageYrBlt_1991.0 GarageYrBlt_1992.0 GarageYrBlt_1993.0 GarageYrBlt_1994.0 GarageYrBlt_1995.0 GarageYrBlt_1996.0 GarageYrBlt_1997.0 GarageYrBlt_1998.0 GarageYrBlt_1999.0 GarageYrBlt_2000.0 GarageYrBlt_2001.0 GarageYrBlt_2002.0 GarageYrBlt_2003.0 GarageYrBlt_2004.0 GarageYrBlt_2005.0 GarageYrBlt_2006.0 GarageYrBlt_2007.0 GarageYrBlt_2008.0 GarageYrBlt_2009.0 GarageYrBlt_2010.0 GarageFinish_None GarageFinish_RFn GarageFinish_Unf GarageQual_Fa GarageQual_Gd GarageQual_None GarageQual_Po GarageQual_TA GarageCond_Fa GarageCond_Gd GarageCond_None GarageCond_Po GarageCond_TA PavedDrive_P PavedDrive_Y PoolQC_Fa PoolQC_Gd PoolQC_None Fence_GdWo Fence_MnPrv Fence_MnWw Fence_None MiscFeature_None MiscFeature_Othr MiscFeature_Shed MiscFeature_TenC MoSold_10 MoSold_11 MoSold_12 MoSold_2 MoSold_3 MoSold_4 MoSold_5 MoSold_6 MoSold_7 MoSold_8 MoSold_9 YrSold_2007 YrSold_2008 YrSold_2009 YrSold_2010 SaleType_CWD SaleType_Con SaleType_ConLD SaleType_ConLI SaleType_ConLw SaleType_New SaleType_Oth SaleType_WD SaleCondition_AdjLand SaleCondition_Alloca SaleCondition_Family SaleCondition_Normal SaleCondition_Partial
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2907 2916 21.0 1894 4 5 0.0 252.0 0.0 294.0 546.0 546 546 0 1092 0.0 0.0 1 1 3 1 6 0 1.0 286.0 0 24 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
2908 2917 160.0 20000 5 7 0.0 1224.0 0.0 0.0 1224.0 1224 0 0 1224 1.0 0.0 1 0 4 1 7 1 2.0 576.0 474 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
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2910 2919 74.0 9627 7 5 94.0 758.0 0.0 238.0 996.0 996 1004 0 2000 0.0 0.0 2 1 3 1 9 1 3.0 650.0 190 48 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0

1459 rows × 561 columns

Join back on the House Prices for the training data.

In [42]:
log_prices = pd.DataFrame(y_train).reset_index().rename({'index':'Id'},axis=1)
log_prices['Id'] = log_prices['Id']+1
train = train.merge(log_prices)
train
Out[42]:
Id LotFrontage LotArea OverallQual OverallCond MasVnrArea BsmtFinSF1 BsmtFinSF2 BsmtUnfSF TotalBsmtSF 1stFlrSF 2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath HalfBath BedroomAbvGr KitchenAbvGr TotRmsAbvGrd Fireplaces GarageCars GarageArea WoodDeckSF OpenPorchSF EnclosedPorch 3SsnPorch ScreenPorch PoolArea MiscVal MSSubClass_150 MSSubClass_160 MSSubClass_180 MSSubClass_190 MSSubClass_20 MSSubClass_30 MSSubClass_40 MSSubClass_45 MSSubClass_50 MSSubClass_60 MSSubClass_70 MSSubClass_75 MSSubClass_80 MSSubClass_85 MSSubClass_90 MSZoning_FV MSZoning_RH MSZoning_RL MSZoning_RM Street_Pave Alley_None Alley_Pave LotShape_IR2 LotShape_IR3 LotShape_Reg LandContour_HLS LandContour_Low LandContour_Lvl Utilities_NoSeWa LotConfig_CulDSac LotConfig_FR2 LotConfig_FR3 LotConfig_Inside LandSlope_Mod LandSlope_Sev Neighborhood_Blueste Neighborhood_BrDale Neighborhood_BrkSide Neighborhood_ClearCr Neighborhood_CollgCr Neighborhood_Crawfor Neighborhood_Edwards Neighborhood_Gilbert Neighborhood_IDOTRR Neighborhood_MeadowV Neighborhood_Mitchel Neighborhood_NAmes Neighborhood_NPkVill Neighborhood_NWAmes Neighborhood_NoRidge Neighborhood_NridgHt Neighborhood_OldTown Neighborhood_SWISU Neighborhood_Sawyer Neighborhood_SawyerW Neighborhood_Somerst Neighborhood_StoneBr Neighborhood_Timber Neighborhood_Veenker Condition1_Feedr Condition1_Norm Condition1_PosA Condition1_PosN Condition1_RRAe Condition1_RRAn Condition1_RRNe Condition1_RRNn Condition2_Feedr Condition2_Norm Condition2_PosA Condition2_PosN Condition2_RRAe Condition2_RRAn Condition2_RRNn BldgType_2fmCon BldgType_Duplex BldgType_Twnhs BldgType_TwnhsE HouseStyle_1.5Unf HouseStyle_1Story HouseStyle_2.5Fin HouseStyle_2.5Unf HouseStyle_2Story HouseStyle_SFoyer HouseStyle_SLvl YearBuilt_1875 YearBuilt_1879 YearBuilt_1880 YearBuilt_1882 YearBuilt_1885 YearBuilt_1890 YearBuilt_1892 YearBuilt_1893 YearBuilt_1895 YearBuilt_1896 YearBuilt_1898 YearBuilt_1900 YearBuilt_1901 YearBuilt_1902 YearBuilt_1904 YearBuilt_1905 YearBuilt_1906 YearBuilt_1907 YearBuilt_1908 YearBuilt_1910 YearBuilt_1911 YearBuilt_1912 YearBuilt_1913 YearBuilt_1914 YearBuilt_1915 YearBuilt_1916 YearBuilt_1917 YearBuilt_1918 YearBuilt_1919 YearBuilt_1920 YearBuilt_1921 YearBuilt_1922 YearBuilt_1923 YearBuilt_1924 YearBuilt_1925 YearBuilt_1926 YearBuilt_1927 YearBuilt_1928 YearBuilt_1929 YearBuilt_1930 YearBuilt_1931 YearBuilt_1932 YearBuilt_1934 YearBuilt_1935 YearBuilt_1936 YearBuilt_1937 YearBuilt_1938 YearBuilt_1939 YearBuilt_1940 YearBuilt_1941 YearBuilt_1942 YearBuilt_1945 YearBuilt_1946 YearBuilt_1947 YearBuilt_1948 YearBuilt_1949 YearBuilt_1950 YearBuilt_1951 YearBuilt_1952 YearBuilt_1953 YearBuilt_1954 YearBuilt_1955 YearBuilt_1956 YearBuilt_1957 YearBuilt_1958 YearBuilt_1959 YearBuilt_1960 YearBuilt_1961 YearBuilt_1962 YearBuilt_1963 YearBuilt_1964 YearBuilt_1965 YearBuilt_1966 YearBuilt_1967 YearBuilt_1968 YearBuilt_1969 YearBuilt_1970 YearBuilt_1971 YearBuilt_1972 YearBuilt_1973 YearBuilt_1974 YearBuilt_1975 YearBuilt_1976 YearBuilt_1977 YearBuilt_1978 YearBuilt_1979 YearBuilt_1980 YearBuilt_1981 YearBuilt_1982 YearBuilt_1983 YearBuilt_1984 YearBuilt_1985 YearBuilt_1986 YearBuilt_1987 YearBuilt_1988 YearBuilt_1989 YearBuilt_1990 YearBuilt_1991 YearBuilt_1992 YearBuilt_1993 YearBuilt_1994 YearBuilt_1995 YearBuilt_1996 YearBuilt_1997 YearBuilt_1998 YearBuilt_1999 YearBuilt_2000 YearBuilt_2001 YearBuilt_2002 YearBuilt_2003 YearBuilt_2004 YearBuilt_2005 YearBuilt_2006 YearBuilt_2007 YearBuilt_2008 YearBuilt_2009 YearBuilt_2010 YearRemodAdd_1951 YearRemodAdd_1952 YearRemodAdd_1953 YearRemodAdd_1954 YearRemodAdd_1955 YearRemodAdd_1956 YearRemodAdd_1957 YearRemodAdd_1958 YearRemodAdd_1959 YearRemodAdd_1960 YearRemodAdd_1961 YearRemodAdd_1962 YearRemodAdd_1963 YearRemodAdd_1964 YearRemodAdd_1965 YearRemodAdd_1966 YearRemodAdd_1967 YearRemodAdd_1968 YearRemodAdd_1969 YearRemodAdd_1970 YearRemodAdd_1971 YearRemodAdd_1972 YearRemodAdd_1973 YearRemodAdd_1974 YearRemodAdd_1975 YearRemodAdd_1976 YearRemodAdd_1977 YearRemodAdd_1978 YearRemodAdd_1979 YearRemodAdd_1980 YearRemodAdd_1981 YearRemodAdd_1982 YearRemodAdd_1983 YearRemodAdd_1984 YearRemodAdd_1985 YearRemodAdd_1986 YearRemodAdd_1987 YearRemodAdd_1988 YearRemodAdd_1989 YearRemodAdd_1990 YearRemodAdd_1991 YearRemodAdd_1992 YearRemodAdd_1993 YearRemodAdd_1994 YearRemodAdd_1995 YearRemodAdd_1996 YearRemodAdd_1997 YearRemodAdd_1998 YearRemodAdd_1999 YearRemodAdd_2000 YearRemodAdd_2001 YearRemodAdd_2002 YearRemodAdd_2003 YearRemodAdd_2004 YearRemodAdd_2005 YearRemodAdd_2006 YearRemodAdd_2007 YearRemodAdd_2008 YearRemodAdd_2009 YearRemodAdd_2010 RoofStyle_Gable RoofStyle_Gambrel RoofStyle_Hip RoofStyle_Mansard RoofStyle_Shed RoofMatl_Membran RoofMatl_Metal RoofMatl_Roll RoofMatl_Tar&Grv RoofMatl_WdShake RoofMatl_WdShngl Exterior1st_AsphShn Exterior1st_BrkComm Exterior1st_BrkFace Exterior1st_CBlock Exterior1st_CemntBd Exterior1st_HdBoard Exterior1st_ImStucc Exterior1st_MetalSd Exterior1st_Plywood Exterior1st_Stone Exterior1st_Stucco Exterior1st_VinylSd Exterior1st_Wd Sdng Exterior1st_WdShing Exterior2nd_AsphShn Exterior2nd_Brk Cmn Exterior2nd_BrkFace Exterior2nd_CBlock Exterior2nd_CmentBd Exterior2nd_HdBoard Exterior2nd_ImStucc Exterior2nd_MetalSd Exterior2nd_Other Exterior2nd_Plywood Exterior2nd_Stone Exterior2nd_Stucco Exterior2nd_VinylSd Exterior2nd_Wd Sdng Exterior2nd_Wd Shng MasVnrType_BrkFace MasVnrType_None MasVnrType_Stone ExterQual_Fa ExterQual_Gd ExterQual_TA ExterCond_Fa ExterCond_Gd ExterCond_Po ExterCond_TA Foundation_CBlock Foundation_PConc Foundation_Slab Foundation_Stone Foundation_Wood BsmtQual_Fa BsmtQual_Gd BsmtQual_None BsmtQual_TA BsmtCond_Gd BsmtCond_None BsmtCond_Po BsmtCond_TA BsmtExposure_Gd BsmtExposure_Mn BsmtExposure_No BsmtExposure_None BsmtFinType1_BLQ BsmtFinType1_GLQ BsmtFinType1_LwQ BsmtFinType1_None BsmtFinType1_Rec BsmtFinType1_Unf BsmtFinType2_BLQ BsmtFinType2_GLQ BsmtFinType2_LwQ BsmtFinType2_None BsmtFinType2_Rec BsmtFinType2_Unf Heating_GasA Heating_GasW Heating_Grav Heating_OthW Heating_Wall HeatingQC_Fa HeatingQC_Gd HeatingQC_Po HeatingQC_TA CentralAir_Y Electrical_FuseF Electrical_FuseP Electrical_Mix Electrical_SBrkr KitchenQual_Fa KitchenQual_Gd KitchenQual_TA Functional_Maj2 Functional_Min1 Functional_Min2 Functional_Mod Functional_Sev Functional_Typ FireplaceQu_Fa FireplaceQu_Gd FireplaceQu_None FireplaceQu_Po FireplaceQu_TA GarageType_Attchd GarageType_Basment GarageType_BuiltIn GarageType_CarPort GarageType_Detchd GarageType_None GarageYrBlt_1896.0 GarageYrBlt_1900.0 GarageYrBlt_1906.0 GarageYrBlt_1908.0 GarageYrBlt_1910.0 GarageYrBlt_1914.0 GarageYrBlt_1915.0 GarageYrBlt_1916.0 GarageYrBlt_1917.0 GarageYrBlt_1918.0 GarageYrBlt_1919.0 GarageYrBlt_1920.0 GarageYrBlt_1921.0 GarageYrBlt_1922.0 GarageYrBlt_1923.0 GarageYrBlt_1924.0 GarageYrBlt_1925.0 GarageYrBlt_1926.0 GarageYrBlt_1927.0 GarageYrBlt_1928.0 GarageYrBlt_1929.0 GarageYrBlt_1930.0 GarageYrBlt_1931.0 GarageYrBlt_1932.0 GarageYrBlt_1933.0 GarageYrBlt_1934.0 GarageYrBlt_1935.0 GarageYrBlt_1936.0 GarageYrBlt_1937.0 GarageYrBlt_1938.0 GarageYrBlt_1939.0 GarageYrBlt_1940.0 GarageYrBlt_1941.0 GarageYrBlt_1942.0 GarageYrBlt_1943.0 GarageYrBlt_1945.0 GarageYrBlt_1946.0 GarageYrBlt_1947.0 GarageYrBlt_1948.0 GarageYrBlt_1949.0 GarageYrBlt_1950.0 GarageYrBlt_1951.0 GarageYrBlt_1952.0 GarageYrBlt_1953.0 GarageYrBlt_1954.0 GarageYrBlt_1955.0 GarageYrBlt_1956.0 GarageYrBlt_1957.0 GarageYrBlt_1958.0 GarageYrBlt_1959.0 GarageYrBlt_1960.0 GarageYrBlt_1961.0 GarageYrBlt_1962.0 GarageYrBlt_1963.0 GarageYrBlt_1964.0 GarageYrBlt_1965.0 GarageYrBlt_1966.0 GarageYrBlt_1967.0 GarageYrBlt_1968.0 GarageYrBlt_1969.0 GarageYrBlt_1970.0 GarageYrBlt_1971.0 GarageYrBlt_1972.0 GarageYrBlt_1973.0 GarageYrBlt_1974.0 GarageYrBlt_1975.0 GarageYrBlt_1976.0 GarageYrBlt_1977.0 GarageYrBlt_1978.0 GarageYrBlt_1979.0 GarageYrBlt_1980.0 GarageYrBlt_1981.0 GarageYrBlt_1982.0 GarageYrBlt_1983.0 GarageYrBlt_1984.0 GarageYrBlt_1985.0 GarageYrBlt_1986.0 GarageYrBlt_1987.0 GarageYrBlt_1988.0 GarageYrBlt_1989.0 GarageYrBlt_1990.0 GarageYrBlt_1991.0 GarageYrBlt_1992.0 GarageYrBlt_1993.0 GarageYrBlt_1994.0 GarageYrBlt_1995.0 GarageYrBlt_1996.0 GarageYrBlt_1997.0 GarageYrBlt_1998.0 GarageYrBlt_1999.0 GarageYrBlt_2000.0 GarageYrBlt_2001.0 GarageYrBlt_2002.0 GarageYrBlt_2003.0 GarageYrBlt_2004.0 GarageYrBlt_2005.0 GarageYrBlt_2006.0 GarageYrBlt_2007.0 GarageYrBlt_2008.0 GarageYrBlt_2009.0 GarageYrBlt_2010.0 GarageFinish_None GarageFinish_RFn GarageFinish_Unf GarageQual_Fa GarageQual_Gd GarageQual_None GarageQual_Po GarageQual_TA GarageCond_Fa GarageCond_Gd GarageCond_None GarageCond_Po GarageCond_TA PavedDrive_P PavedDrive_Y PoolQC_Fa PoolQC_Gd PoolQC_None Fence_GdWo Fence_MnPrv Fence_MnWw Fence_None MiscFeature_None MiscFeature_Othr MiscFeature_Shed MiscFeature_TenC MoSold_10 MoSold_11 MoSold_12 MoSold_2 MoSold_3 MoSold_4 MoSold_5 MoSold_6 MoSold_7 MoSold_8 MoSold_9 YrSold_2007 YrSold_2008 YrSold_2009 YrSold_2010 SaleType_CWD SaleType_Con SaleType_ConLD SaleType_ConLI SaleType_ConLw SaleType_New SaleType_Oth SaleType_WD SaleCondition_AdjLand SaleCondition_Alloca SaleCondition_Family SaleCondition_Normal SaleCondition_Partial LogSalePrice
0 1 65.0 8450 7 5 196.0 706.0 0.0 150.0 856.0 856 854 0 1710 1.0 0.0 2 1 3 1 8 0 2.0 548.0 0 61 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 12.247694
1 2 80.0 9600 6 8 0.0 978.0 0.0 284.0 1262.0 1262 0 0 1262 0.0 1.0 2 0 3 1 6 1 2.0 460.0 298 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 12.109011
2 3 68.0 11250 7 5 162.0 486.0 0.0 434.0 920.0 920 866 0 1786 1.0 0.0 2 1 3 1 6 1 2.0 608.0 0 42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 12.317167
3 4 60.0 9550 7 5 0.0 216.0 0.0 540.0 756.0 961 756 0 1717 1.0 0.0 1 0 3 1 7 1 3.0 642.0 0 35 272 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 11.849398
4 5 84.0 14260 8 5 350.0 655.0 0.0 490.0 1145.0 1145 1053 0 2198 1.0 0.0 2 1 4 1 9 1 3.0 836.0 192 84 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 12.429216
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
1447 1456 62.0 7917 6 5 0.0 0.0 0.0 953.0 953.0 953 694 0 1647 0.0 0.0 2 1 3 1 7 1 2.0 460.0 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 12.072541
1448 1457 85.0 13175 6 6 119.0 790.0 163.0 589.0 1542.0 2073 0 0 2073 1.0 0.0 2 0 3 1 7 2 2.0 500.0 349 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 12.254863
1449 1458 66.0 9042 7 9 0.0 275.0 0.0 877.0 1152.0 1188 1152 0 2340 0.0 0.0 2 0 4 1 9 2 1.0 252.0 0 60 0 0 0 0 2500 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 12.493130
1450 1459 68.0 9717 5 6 0.0 49.0 1029.0 0.0 1078.0 1078 0 0 1078 1.0 0.0 1 0 2 1 5 0 1.0 240.0 366 0 112 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 11.864462
1451 1460 75.0 9937 5 6 0.0 830.0 290.0 136.0 1256.0 1256 0 0 1256 1.0 0.0 1 1 3 1 6 0 1.0 276.0 736 68 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 11.901583

1452 rows × 562 columns

Model 1: Univariate Linear Regression: Ground Floor Area to Predict Sale Price

One can imagine that the Size of the House will be related to the Price. As a first attempt, let's focus on a single variable. Build a model with all of the training data, apply this to the test data and submit to put a mark on the leaderboard.

In [43]:
px.scatter(train,x='GrLivArea',y='LogSalePrice',title='Ground Floor Area vs. Log Sale Price')
In [44]:
model = LinearRegression(normalize = True)  
model.fit(train[['GrLivArea']], y_train) #training the algorithm
print('Model Intercept:',round(model.intercept_,2))
print('Model Slope:', round(model.coef_[0],2))
Out[44]:
LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=True)
Model Intercept: 11.16
Model Slope: 0.0
In [45]:
np.exp(model.predict(test[['GrLivArea']])) # Out put the predictions for the test set.
Out[45]:
array([117365.94367828, 150179.6228743 , 178152.82165401, ...,
       141464.48271672, 122416.58124591, 220054.74408825])
In [46]:
test['Log_Predictions'] = model.predict(test[['GrLivArea']])
test['Predictions'] = np.exp(test['Log_Predictions'])

test
Out[46]:
Id LotFrontage LotArea OverallQual OverallCond MasVnrArea BsmtFinSF1 BsmtFinSF2 BsmtUnfSF TotalBsmtSF 1stFlrSF 2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath HalfBath BedroomAbvGr KitchenAbvGr TotRmsAbvGrd Fireplaces GarageCars GarageArea WoodDeckSF OpenPorchSF EnclosedPorch 3SsnPorch ScreenPorch PoolArea MiscVal MSSubClass_150 MSSubClass_160 MSSubClass_180 MSSubClass_190 MSSubClass_20 MSSubClass_30 MSSubClass_40 MSSubClass_45 MSSubClass_50 MSSubClass_60 MSSubClass_70 MSSubClass_75 MSSubClass_80 MSSubClass_85 MSSubClass_90 MSZoning_FV MSZoning_RH MSZoning_RL MSZoning_RM Street_Pave Alley_None Alley_Pave LotShape_IR2 LotShape_IR3 LotShape_Reg LandContour_HLS LandContour_Low LandContour_Lvl Utilities_NoSeWa LotConfig_CulDSac LotConfig_FR2 LotConfig_FR3 LotConfig_Inside LandSlope_Mod LandSlope_Sev Neighborhood_Blueste Neighborhood_BrDale Neighborhood_BrkSide Neighborhood_ClearCr Neighborhood_CollgCr Neighborhood_Crawfor Neighborhood_Edwards Neighborhood_Gilbert Neighborhood_IDOTRR Neighborhood_MeadowV Neighborhood_Mitchel Neighborhood_NAmes Neighborhood_NPkVill Neighborhood_NWAmes Neighborhood_NoRidge Neighborhood_NridgHt Neighborhood_OldTown Neighborhood_SWISU Neighborhood_Sawyer Neighborhood_SawyerW Neighborhood_Somerst Neighborhood_StoneBr Neighborhood_Timber Neighborhood_Veenker Condition1_Feedr Condition1_Norm Condition1_PosA Condition1_PosN Condition1_RRAe Condition1_RRAn Condition1_RRNe Condition1_RRNn Condition2_Feedr Condition2_Norm Condition2_PosA Condition2_PosN Condition2_RRAe Condition2_RRAn Condition2_RRNn BldgType_2fmCon BldgType_Duplex BldgType_Twnhs BldgType_TwnhsE HouseStyle_1.5Unf HouseStyle_1Story HouseStyle_2.5Fin HouseStyle_2.5Unf HouseStyle_2Story HouseStyle_SFoyer HouseStyle_SLvl YearBuilt_1875 YearBuilt_1879 YearBuilt_1880 YearBuilt_1882 YearBuilt_1885 YearBuilt_1890 YearBuilt_1892 YearBuilt_1893 YearBuilt_1895 YearBuilt_1896 YearBuilt_1898 YearBuilt_1900 YearBuilt_1901 YearBuilt_1902 YearBuilt_1904 YearBuilt_1905 YearBuilt_1906 YearBuilt_1907 YearBuilt_1908 YearBuilt_1910 YearBuilt_1911 YearBuilt_1912 YearBuilt_1913 YearBuilt_1914 YearBuilt_1915 YearBuilt_1916 YearBuilt_1917 YearBuilt_1918 YearBuilt_1919 YearBuilt_1920 YearBuilt_1921 YearBuilt_1922 YearBuilt_1923 YearBuilt_1924 YearBuilt_1925 YearBuilt_1926 YearBuilt_1927 YearBuilt_1928 YearBuilt_1929 YearBuilt_1930 YearBuilt_1931 YearBuilt_1932 YearBuilt_1934 YearBuilt_1935 YearBuilt_1936 YearBuilt_1937 YearBuilt_1938 YearBuilt_1939 YearBuilt_1940 YearBuilt_1941 YearBuilt_1942 YearBuilt_1945 YearBuilt_1946 YearBuilt_1947 YearBuilt_1948 YearBuilt_1949 YearBuilt_1950 YearBuilt_1951 YearBuilt_1952 YearBuilt_1953 YearBuilt_1954 YearBuilt_1955 YearBuilt_1956 YearBuilt_1957 YearBuilt_1958 YearBuilt_1959 YearBuilt_1960 YearBuilt_1961 YearBuilt_1962 YearBuilt_1963 YearBuilt_1964 YearBuilt_1965 YearBuilt_1966 YearBuilt_1967 YearBuilt_1968 YearBuilt_1969 YearBuilt_1970 YearBuilt_1971 YearBuilt_1972 YearBuilt_1973 YearBuilt_1974 YearBuilt_1975 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GarageYrBlt_1988.0 GarageYrBlt_1989.0 GarageYrBlt_1990.0 GarageYrBlt_1991.0 GarageYrBlt_1992.0 GarageYrBlt_1993.0 GarageYrBlt_1994.0 GarageYrBlt_1995.0 GarageYrBlt_1996.0 GarageYrBlt_1997.0 GarageYrBlt_1998.0 GarageYrBlt_1999.0 GarageYrBlt_2000.0 GarageYrBlt_2001.0 GarageYrBlt_2002.0 GarageYrBlt_2003.0 GarageYrBlt_2004.0 GarageYrBlt_2005.0 GarageYrBlt_2006.0 GarageYrBlt_2007.0 GarageYrBlt_2008.0 GarageYrBlt_2009.0 GarageYrBlt_2010.0 GarageFinish_None GarageFinish_RFn GarageFinish_Unf GarageQual_Fa GarageQual_Gd GarageQual_None GarageQual_Po GarageQual_TA GarageCond_Fa GarageCond_Gd GarageCond_None GarageCond_Po GarageCond_TA PavedDrive_P PavedDrive_Y PoolQC_Fa PoolQC_Gd PoolQC_None Fence_GdWo Fence_MnPrv Fence_MnWw Fence_None MiscFeature_None MiscFeature_Othr MiscFeature_Shed MiscFeature_TenC MoSold_10 MoSold_11 MoSold_12 MoSold_2 MoSold_3 MoSold_4 MoSold_5 MoSold_6 MoSold_7 MoSold_8 MoSold_9 YrSold_2007 YrSold_2008 YrSold_2009 YrSold_2010 SaleType_CWD SaleType_Con SaleType_ConLD SaleType_ConLI SaleType_ConLw SaleType_New SaleType_Oth SaleType_WD SaleCondition_AdjLand SaleCondition_Alloca SaleCondition_Family SaleCondition_Normal SaleCondition_Partial Log_Predictions Predictions
1452 1461 80.0 11622 5 6 0.0 468.0 144.0 270.0 882.0 896 0 0 896 0.0 0.0 1 0 2 1 5 0 1.0 730.0 140 0 0 0 120 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 11.673052 117365.943678
1453 1462 81.0 14267 6 6 108.0 923.0 0.0 406.0 1329.0 1329 0 0 1329 0.0 0.0 1 1 3 1 6 0 1.0 312.0 393 36 0 0 0 0 12500 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 11.919587 150179.622874
1454 1463 74.0 13830 5 5 0.0 791.0 0.0 137.0 928.0 928 701 0 1629 0.0 0.0 2 1 3 1 6 1 2.0 482.0 212 34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 12.090397 178152.821654
1455 1464 78.0 9978 6 6 20.0 602.0 0.0 324.0 926.0 926 678 0 1604 0.0 0.0 2 1 3 1 7 1 2.0 470.0 360 36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 12.076163 175634.932148
1456 1465 43.0 5005 8 5 0.0 263.0 0.0 1017.0 1280.0 1280 0 0 1280 0.0 0.0 2 0 2 1 5 0 2.0 506.0 0 82 0 0 144 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 11.891688 146047.681094
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
2906 2915 21.0 1936 4 7 0.0 0.0 0.0 546.0 546.0 546 546 0 1092 0.0 0.0 1 1 3 1 5 0 0.0 0.0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 11.784648 131222.246849
2907 2916 21.0 1894 4 5 0.0 252.0 0.0 294.0 546.0 546 546 0 1092 0.0 0.0 1 1 3 1 6 0 1.0 286.0 0 24 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 11.784648 131222.246849
2908 2917 160.0 20000 5 7 0.0 1224.0 0.0 0.0 1224.0 1224 0 0 1224 1.0 0.0 1 0 4 1 7 1 2.0 576.0 474 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 11.859804 141464.482717
2909 2918 62.0 10441 5 5 0.0 337.0 0.0 575.0 912.0 970 0 0 970 0.0 1.0 1 0 3 1 6 0 0.0 0.0 80 32 0 0 0 0 700 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 11.715185 122416.581246
2910 2919 74.0 9627 7 5 94.0 758.0 0.0 238.0 996.0 996 1004 0 2000 0.0 0.0 2 1 3 1 9 1 3.0 650.0 190 48 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 12.301632 220054.744088

1459 rows × 563 columns

In [47]:
fig = go.Figure(data=go.Scatter(
                x=train['GrLivArea'],
                y=train['LogSalePrice'],
                mode='markers',
                name = 'Data',
                hovertemplate='Living Area: %{x} <br>Log Sale Price: %{y} '
));

fig.add_trace(go.Scatter(
                x=test['GrLivArea'],
                y=test['Log_Predictions'],
                mode='markers',
                name = 'Predictions',
                hovertemplate='Living Area: %{x} <br>Log Prediction: %{y} '
));

fig.update_layout(
    title='Univariate Regression Line: Ground Floor Size vs. Sale Price',
    xaxis_title='Ground Floor Living Area/(Sq.ft)',
    yaxis_title='Log Sale Price/$'
)

Result

An Improvement of a 0.40890 RMSE to a 0.29403 RMSE. This pushed me into 3,800th up from 4200th.

Model 2: Multivariate Linear Regression

I'm going to split my test set into a training set and a validation set with a 75:25 split.

I will then build my models with the training set data, and will then assess each models performance on the validation set. With this method, I can have a fairer view on model performance, and on the bias / variance trade-off.

I can explore the impact of changing the model features, changing the regularisation parameter, and even experimenting with neural networks. and have a fairer view on model performance.

Then, the best models can be used to predict the house prices in the test set.

In [48]:
train
Out[48]:
Id LotFrontage LotArea OverallQual OverallCond MasVnrArea BsmtFinSF1 BsmtFinSF2 BsmtUnfSF TotalBsmtSF 1stFlrSF 2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath HalfBath BedroomAbvGr KitchenAbvGr TotRmsAbvGrd Fireplaces GarageCars GarageArea WoodDeckSF OpenPorchSF EnclosedPorch 3SsnPorch ScreenPorch PoolArea MiscVal MSSubClass_150 MSSubClass_160 MSSubClass_180 MSSubClass_190 MSSubClass_20 MSSubClass_30 MSSubClass_40 MSSubClass_45 MSSubClass_50 MSSubClass_60 MSSubClass_70 MSSubClass_75 MSSubClass_80 MSSubClass_85 MSSubClass_90 MSZoning_FV MSZoning_RH MSZoning_RL MSZoning_RM Street_Pave Alley_None Alley_Pave LotShape_IR2 LotShape_IR3 LotShape_Reg LandContour_HLS LandContour_Low LandContour_Lvl Utilities_NoSeWa LotConfig_CulDSac LotConfig_FR2 LotConfig_FR3 LotConfig_Inside LandSlope_Mod LandSlope_Sev Neighborhood_Blueste Neighborhood_BrDale Neighborhood_BrkSide Neighborhood_ClearCr Neighborhood_CollgCr Neighborhood_Crawfor Neighborhood_Edwards Neighborhood_Gilbert Neighborhood_IDOTRR Neighborhood_MeadowV Neighborhood_Mitchel Neighborhood_NAmes Neighborhood_NPkVill Neighborhood_NWAmes Neighborhood_NoRidge Neighborhood_NridgHt Neighborhood_OldTown Neighborhood_SWISU Neighborhood_Sawyer Neighborhood_SawyerW Neighborhood_Somerst Neighborhood_StoneBr Neighborhood_Timber Neighborhood_Veenker Condition1_Feedr Condition1_Norm Condition1_PosA Condition1_PosN Condition1_RRAe Condition1_RRAn Condition1_RRNe Condition1_RRNn Condition2_Feedr Condition2_Norm Condition2_PosA Condition2_PosN Condition2_RRAe Condition2_RRAn Condition2_RRNn BldgType_2fmCon BldgType_Duplex BldgType_Twnhs BldgType_TwnhsE HouseStyle_1.5Unf HouseStyle_1Story HouseStyle_2.5Fin HouseStyle_2.5Unf HouseStyle_2Story HouseStyle_SFoyer HouseStyle_SLvl YearBuilt_1875 YearBuilt_1879 YearBuilt_1880 YearBuilt_1882 YearBuilt_1885 YearBuilt_1890 YearBuilt_1892 YearBuilt_1893 YearBuilt_1895 YearBuilt_1896 YearBuilt_1898 YearBuilt_1900 YearBuilt_1901 YearBuilt_1902 YearBuilt_1904 YearBuilt_1905 YearBuilt_1906 YearBuilt_1907 YearBuilt_1908 YearBuilt_1910 YearBuilt_1911 YearBuilt_1912 YearBuilt_1913 YearBuilt_1914 YearBuilt_1915 YearBuilt_1916 YearBuilt_1917 YearBuilt_1918 YearBuilt_1919 YearBuilt_1920 YearBuilt_1921 YearBuilt_1922 YearBuilt_1923 YearBuilt_1924 YearBuilt_1925 YearBuilt_1926 YearBuilt_1927 YearBuilt_1928 YearBuilt_1929 YearBuilt_1930 YearBuilt_1931 YearBuilt_1932 YearBuilt_1934 YearBuilt_1935 YearBuilt_1936 YearBuilt_1937 YearBuilt_1938 YearBuilt_1939 YearBuilt_1940 YearBuilt_1941 YearBuilt_1942 YearBuilt_1945 YearBuilt_1946 YearBuilt_1947 YearBuilt_1948 YearBuilt_1949 YearBuilt_1950 YearBuilt_1951 YearBuilt_1952 YearBuilt_1953 YearBuilt_1954 YearBuilt_1955 YearBuilt_1956 YearBuilt_1957 YearBuilt_1958 YearBuilt_1959 YearBuilt_1960 YearBuilt_1961 YearBuilt_1962 YearBuilt_1963 YearBuilt_1964 YearBuilt_1965 YearBuilt_1966 YearBuilt_1967 YearBuilt_1968 YearBuilt_1969 YearBuilt_1970 YearBuilt_1971 YearBuilt_1972 YearBuilt_1973 YearBuilt_1974 YearBuilt_1975 YearBuilt_1976 YearBuilt_1977 YearBuilt_1978 YearBuilt_1979 YearBuilt_1980 YearBuilt_1981 YearBuilt_1982 YearBuilt_1983 YearBuilt_1984 YearBuilt_1985 YearBuilt_1986 YearBuilt_1987 YearBuilt_1988 YearBuilt_1989 YearBuilt_1990 YearBuilt_1991 YearBuilt_1992 YearBuilt_1993 YearBuilt_1994 YearBuilt_1995 YearBuilt_1996 YearBuilt_1997 YearBuilt_1998 YearBuilt_1999 YearBuilt_2000 YearBuilt_2001 YearBuilt_2002 YearBuilt_2003 YearBuilt_2004 YearBuilt_2005 YearBuilt_2006 YearBuilt_2007 YearBuilt_2008 YearBuilt_2009 YearBuilt_2010 YearRemodAdd_1951 YearRemodAdd_1952 YearRemodAdd_1953 YearRemodAdd_1954 YearRemodAdd_1955 YearRemodAdd_1956 YearRemodAdd_1957 YearRemodAdd_1958 YearRemodAdd_1959 YearRemodAdd_1960 YearRemodAdd_1961 YearRemodAdd_1962 YearRemodAdd_1963 YearRemodAdd_1964 YearRemodAdd_1965 YearRemodAdd_1966 YearRemodAdd_1967 YearRemodAdd_1968 YearRemodAdd_1969 YearRemodAdd_1970 YearRemodAdd_1971 YearRemodAdd_1972 YearRemodAdd_1973 YearRemodAdd_1974 YearRemodAdd_1975 YearRemodAdd_1976 YearRemodAdd_1977 YearRemodAdd_1978 YearRemodAdd_1979 YearRemodAdd_1980 YearRemodAdd_1981 YearRemodAdd_1982 YearRemodAdd_1983 YearRemodAdd_1984 YearRemodAdd_1985 YearRemodAdd_1986 YearRemodAdd_1987 YearRemodAdd_1988 YearRemodAdd_1989 YearRemodAdd_1990 YearRemodAdd_1991 YearRemodAdd_1992 YearRemodAdd_1993 YearRemodAdd_1994 YearRemodAdd_1995 YearRemodAdd_1996 YearRemodAdd_1997 YearRemodAdd_1998 YearRemodAdd_1999 YearRemodAdd_2000 YearRemodAdd_2001 YearRemodAdd_2002 YearRemodAdd_2003 YearRemodAdd_2004 YearRemodAdd_2005 YearRemodAdd_2006 YearRemodAdd_2007 YearRemodAdd_2008 YearRemodAdd_2009 YearRemodAdd_2010 RoofStyle_Gable RoofStyle_Gambrel RoofStyle_Hip RoofStyle_Mansard RoofStyle_Shed RoofMatl_Membran RoofMatl_Metal RoofMatl_Roll RoofMatl_Tar&Grv RoofMatl_WdShake RoofMatl_WdShngl Exterior1st_AsphShn Exterior1st_BrkComm Exterior1st_BrkFace Exterior1st_CBlock Exterior1st_CemntBd Exterior1st_HdBoard Exterior1st_ImStucc Exterior1st_MetalSd Exterior1st_Plywood Exterior1st_Stone Exterior1st_Stucco Exterior1st_VinylSd Exterior1st_Wd Sdng Exterior1st_WdShing Exterior2nd_AsphShn Exterior2nd_Brk Cmn Exterior2nd_BrkFace Exterior2nd_CBlock Exterior2nd_CmentBd Exterior2nd_HdBoard Exterior2nd_ImStucc Exterior2nd_MetalSd Exterior2nd_Other Exterior2nd_Plywood Exterior2nd_Stone Exterior2nd_Stucco Exterior2nd_VinylSd Exterior2nd_Wd Sdng Exterior2nd_Wd Shng MasVnrType_BrkFace MasVnrType_None MasVnrType_Stone ExterQual_Fa ExterQual_Gd ExterQual_TA ExterCond_Fa ExterCond_Gd ExterCond_Po ExterCond_TA Foundation_CBlock Foundation_PConc Foundation_Slab Foundation_Stone Foundation_Wood BsmtQual_Fa BsmtQual_Gd BsmtQual_None BsmtQual_TA BsmtCond_Gd BsmtCond_None BsmtCond_Po BsmtCond_TA BsmtExposure_Gd BsmtExposure_Mn BsmtExposure_No BsmtExposure_None BsmtFinType1_BLQ BsmtFinType1_GLQ BsmtFinType1_LwQ BsmtFinType1_None BsmtFinType1_Rec BsmtFinType1_Unf BsmtFinType2_BLQ BsmtFinType2_GLQ BsmtFinType2_LwQ BsmtFinType2_None BsmtFinType2_Rec BsmtFinType2_Unf Heating_GasA Heating_GasW Heating_Grav Heating_OthW Heating_Wall HeatingQC_Fa HeatingQC_Gd HeatingQC_Po HeatingQC_TA CentralAir_Y Electrical_FuseF Electrical_FuseP Electrical_Mix Electrical_SBrkr KitchenQual_Fa KitchenQual_Gd KitchenQual_TA Functional_Maj2 Functional_Min1 Functional_Min2 Functional_Mod Functional_Sev Functional_Typ FireplaceQu_Fa FireplaceQu_Gd FireplaceQu_None FireplaceQu_Po FireplaceQu_TA GarageType_Attchd GarageType_Basment GarageType_BuiltIn GarageType_CarPort GarageType_Detchd GarageType_None GarageYrBlt_1896.0 GarageYrBlt_1900.0 GarageYrBlt_1906.0 GarageYrBlt_1908.0 GarageYrBlt_1910.0 GarageYrBlt_1914.0 GarageYrBlt_1915.0 GarageYrBlt_1916.0 GarageYrBlt_1917.0 GarageYrBlt_1918.0 GarageYrBlt_1919.0 GarageYrBlt_1920.0 GarageYrBlt_1921.0 GarageYrBlt_1922.0 GarageYrBlt_1923.0 GarageYrBlt_1924.0 GarageYrBlt_1925.0 GarageYrBlt_1926.0 GarageYrBlt_1927.0 GarageYrBlt_1928.0 GarageYrBlt_1929.0 GarageYrBlt_1930.0 GarageYrBlt_1931.0 GarageYrBlt_1932.0 GarageYrBlt_1933.0 GarageYrBlt_1934.0 GarageYrBlt_1935.0 GarageYrBlt_1936.0 GarageYrBlt_1937.0 GarageYrBlt_1938.0 GarageYrBlt_1939.0 GarageYrBlt_1940.0 GarageYrBlt_1941.0 GarageYrBlt_1942.0 GarageYrBlt_1943.0 GarageYrBlt_1945.0 GarageYrBlt_1946.0 GarageYrBlt_1947.0 GarageYrBlt_1948.0 GarageYrBlt_1949.0 GarageYrBlt_1950.0 GarageYrBlt_1951.0 GarageYrBlt_1952.0 GarageYrBlt_1953.0 GarageYrBlt_1954.0 GarageYrBlt_1955.0 GarageYrBlt_1956.0 GarageYrBlt_1957.0 GarageYrBlt_1958.0 GarageYrBlt_1959.0 GarageYrBlt_1960.0 GarageYrBlt_1961.0 GarageYrBlt_1962.0 GarageYrBlt_1963.0 GarageYrBlt_1964.0 GarageYrBlt_1965.0 GarageYrBlt_1966.0 GarageYrBlt_1967.0 GarageYrBlt_1968.0 GarageYrBlt_1969.0 GarageYrBlt_1970.0 GarageYrBlt_1971.0 GarageYrBlt_1972.0 GarageYrBlt_1973.0 GarageYrBlt_1974.0 GarageYrBlt_1975.0 GarageYrBlt_1976.0 GarageYrBlt_1977.0 GarageYrBlt_1978.0 GarageYrBlt_1979.0 GarageYrBlt_1980.0 GarageYrBlt_1981.0 GarageYrBlt_1982.0 GarageYrBlt_1983.0 GarageYrBlt_1984.0 GarageYrBlt_1985.0 GarageYrBlt_1986.0 GarageYrBlt_1987.0 GarageYrBlt_1988.0 GarageYrBlt_1989.0 GarageYrBlt_1990.0 GarageYrBlt_1991.0 GarageYrBlt_1992.0 GarageYrBlt_1993.0 GarageYrBlt_1994.0 GarageYrBlt_1995.0 GarageYrBlt_1996.0 GarageYrBlt_1997.0 GarageYrBlt_1998.0 GarageYrBlt_1999.0 GarageYrBlt_2000.0 GarageYrBlt_2001.0 GarageYrBlt_2002.0 GarageYrBlt_2003.0 GarageYrBlt_2004.0 GarageYrBlt_2005.0 GarageYrBlt_2006.0 GarageYrBlt_2007.0 GarageYrBlt_2008.0 GarageYrBlt_2009.0 GarageYrBlt_2010.0 GarageFinish_None GarageFinish_RFn GarageFinish_Unf GarageQual_Fa GarageQual_Gd GarageQual_None GarageQual_Po GarageQual_TA GarageCond_Fa GarageCond_Gd GarageCond_None GarageCond_Po GarageCond_TA PavedDrive_P PavedDrive_Y PoolQC_Fa PoolQC_Gd PoolQC_None Fence_GdWo Fence_MnPrv Fence_MnWw Fence_None MiscFeature_None MiscFeature_Othr MiscFeature_Shed MiscFeature_TenC MoSold_10 MoSold_11 MoSold_12 MoSold_2 MoSold_3 MoSold_4 MoSold_5 MoSold_6 MoSold_7 MoSold_8 MoSold_9 YrSold_2007 YrSold_2008 YrSold_2009 YrSold_2010 SaleType_CWD SaleType_Con SaleType_ConLD SaleType_ConLI SaleType_ConLw SaleType_New SaleType_Oth SaleType_WD SaleCondition_AdjLand SaleCondition_Alloca SaleCondition_Family SaleCondition_Normal SaleCondition_Partial LogSalePrice
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1447 1456 62.0 7917 6 5 0.0 0.0 0.0 953.0 953.0 953 694 0 1647 0.0 0.0 2 1 3 1 7 1 2.0 460.0 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 12.072541
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1452 rows × 562 columns

In [49]:
X_train, X_val, y_train, y_val = train_test_split(train.drop(['Id','LogSalePrice'],axis=1), train['LogSalePrice'], test_size=0.25, random_state=42)
In [50]:
model = LinearRegression(normalize = True,)  
model.fit(X_train, y_train) # Fit the model to the training data
print('Model Intercept:',round(model.intercept_,2))
print('Model Coefficients:', model.coef_)
Out[50]:
LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=True)
Model Intercept: -16717754167.21
Model Coefficients: [ 4.20015089e-04  3.93673720e-06  2.00961736e-02  5.05119510e-02
  2.95032069e-05  9.82337781e+07  9.82337781e+07  9.82337781e+07
 -9.82337781e+07  8.88878096e+07  8.88878096e+07  8.88878096e+07
 -8.88878096e+07  2.51853417e-02  3.19579095e-02  3.29309966e-02
  1.79235893e-02 -1.15175877e-02  3.26693460e-02  5.09981116e-03
  3.14197421e-02  3.34852713e-02  6.32292831e-05  9.62348008e-05
  1.42507662e-04  1.89860775e-06  1.11494049e-04  2.80854332e-04
  1.54117986e-03 -3.99133581e-05 -4.00135520e+11 -7.64246394e-02
 -4.69600611e-02  6.40282267e-01  1.14246340e-01  9.01302849e-02
  2.43773508e-01  2.23828366e-01  2.63553264e-01  6.18739008e-02
  1.16932416e-01  6.21165659e-02  1.89693976e-02  1.20632107e-01
  1.02009010e+11  5.70044527e-01  4.95876410e-01  5.23047251e-01
  4.27567689e-01  1.05991652e-01 -2.66533322e-02 -3.98267292e-02
  4.98902984e-03  2.47967197e-02  2.78045708e-02  4.64766261e-02
  2.83130207e-02  2.44596578e-02 -3.85056900e-01  3.72306159e-02
 -4.46986564e-02 -5.90885881e-02 -1.30654744e-02  2.59142489e-02
 -2.49152676e-01 -5.83077222e-02  5.67836833e-02  5.56351627e-02
  4.44168810e-02 -7.89404084e-03  1.26083414e-01 -3.92896176e-02
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  8.00110406e-02  1.67832989e-02 -2.30663167e-02  2.90417041e-03
  2.76684712e-03  2.43590026e-02  1.30303257e-01  3.11626928e-02
  1.84100550e-02  1.08141067e-01  1.28734760e-01  1.27305530e-01
  1.69627917e-01  1.23997135e-03  1.22281526e-01  1.23725491e-01
  1.51875252e-01  3.49488495e-01  1.85970584e-01  1.12656026e+11
  3.54929844e-04 -3.84179117e-01  5.16300302e+09 -3.05759056e+10
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  4.09512279e-02  9.89504346e-02 -4.28517213e-03  3.59223491e-01
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  9.21821602e+09  9.21821602e+09 -1.03437810e+11 -2.28130443e+10
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 -1.59979765e+09  9.21821602e+09  9.21821602e+09 -1.55100661e+10
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  9.21821602e+09  9.21821602e+09  9.21821602e+09  9.21821602e+09
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In [51]:
train_results = pd.DataFrame(y_train)
train_results['Model_Output(Log)'] = model.predict(X_train)
print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(train_results['LogSalePrice'], train_results['Model_Output(Log)'])))
Root Mean Squared Error: 0.06738022470800617
In [52]:
train_results.head()
Out[52]:
LogSalePrice Model_Output(Log)
1043 11.349229 11.413496
481 11.898188 11.840372
886 11.947949 11.947662
54 11.775290 11.723879
968 12.028739 12.134094
In [53]:
px.scatter(train_results,x='Model_Output(Log)',y='LogSalePrice',title='Multivariate Regression Training Predictions')

Testing the model on my validation set:

In [54]:
val_results = pd.DataFrame(y_val)
val_results['Model_Predictions(Log)'] = model.predict(X_val)
print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(val_results['LogSalePrice'], val_results['Model_Predictions(Log)'])))
Root Mean Squared Error: 9589855245.604158
In [55]:
px.scatter(val_results,x='Model_Predictions(Log)',y='LogSalePrice',title='Multivariate Regression Validation Predictions')
In [56]:
val_results
Out[56]:
LogSalePrice Model_Predictions(Log)
1036 12.185870 1.220246e+01
1124 11.813030 -6.826064e+10
997 11.827043 5.163003e+09
1316 11.320554 1.176862e+01
529 12.089539 1.209618e+01
... ... ...
514 12.259613 1.229887e+01
722 11.608236 1.219272e+01
841 11.801857 1.174449e+01
1079 11.898188 1.195797e+01
1377 11.561716 1.167438e+01

363 rows × 2 columns

Result

An Improvement of a 0.29403 RMSE to a 0.28935 RMSE, with a bit of manual value imputing for the values predicted as 0 or infinity! This pushed me up 11 places, negligible. I know I can do better!

This appears to be overfitting, and I'm not surprised. I have more feature variables than houses in my validation set. More concerning are the 0 value predictions. One way to handle over-fitting (high variance) is through regularisation (penalising large parameter values). I will try this next.

Model 3: Introducing the Regularisation Parameter, Ridge, Alpha = 1

Ridge uses L2 penalties (square of the coefficients)

In [57]:
model = Ridge(alpha=1, fit_intercept=True)
model.fit(X_train, y_train) # Fit the model to the training data
print('Model Intercept:',round(model.intercept_,2))
print('Model Coefficients:', model.coef_)
Out[57]:
Ridge(alpha=1, copy_X=True, fit_intercept=True, max_iter=None, normalize=False,
      random_state=None, solver='auto', tol=0.001)
Model Intercept: 10.16
Model Coefficients: [ 4.71227463e-04  4.42800956e-06  3.17560772e-02  4.78945122e-02
  6.97842888e-06  6.56376522e-05  5.26054297e-05 -3.96727545e-06
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  4.15023510e-02  2.76078968e-02  4.55388352e-02 -1.77771704e-02
  7.36022446e-02  5.20740678e-02 -4.17258228e-04 -1.01348192e-02
 -1.29143345e-02  5.01360913e-02  7.31402209e-03  3.64881152e-02
  9.99207000e-03 -2.20341253e-02  1.74459858e-02 -3.56676105e-02
  1.14426997e-02  4.69609453e-03  3.82716010e-02 -2.14440453e-02
  3.06438673e-02  2.06754102e-02  4.15048158e-02  4.48775251e-02
 -1.99136036e-02 -2.84288281e-02  1.51392940e-02 -3.01922330e-02
  1.37586838e-02 -9.39544727e-03  9.93398038e-04  3.74051155e-02
  4.64125346e-03  7.50842690e-03 -3.71508974e-02  5.42439717e-03
 -2.97853452e-02  8.92196866e-03 -3.80686889e-02  1.43977611e-02
  8.92196866e-03  5.76446002e-02  2.27876367e-02  3.16952890e-02
  7.00323365e-03  1.99301574e-04  8.92196866e-03  6.49831368e-03
  2.82590936e-03 -1.56728261e-02  8.92196866e-03 -2.16545912e-02
 -2.28374341e-02 -4.29481450e-02  4.11398185e-02 -5.22007378e-03
 -2.57328254e-02  3.74121102e-03  2.28123683e-02  7.93178710e-02
  8.05041649e-02 -6.19800595e-02 -3.24817577e-02  1.29557524e-03
  5.70227091e-04 -2.94835986e-02  2.23713347e-02 -2.74620681e-02
  8.00752173e-02  9.33475808e-03 -1.68546344e-02 -1.03106411e-02
 -1.48357524e-02 -4.60062695e-02 -3.93313213e-02 -4.72455329e-02
 -1.01100933e-01  4.23742437e-02  6.05761502e-02 -4.76346624e-02
  0.00000000e+00  9.06955285e-02 -3.61793076e-02 -5.50836868e-03
 -7.68303534e-03 -1.57413353e-02 -1.61268449e-02  6.59620970e-02
  2.80464845e-02  6.48563549e-02 -3.67129814e-02  3.88269369e-02
 -1.39429114e-03  0.00000000e+00 -1.81318167e-02 -2.20506062e-02
 -2.71864403e-02  3.18958083e-02 -2.01996965e-02 -4.08687093e-02
 -9.66154445e-02  0.00000000e+00 -4.30261844e-02  0.00000000e+00
  4.90021003e-02  2.35677631e-02  7.94330178e-02  8.11903327e-03
 -5.83058832e-02 -1.41377339e-02  4.67312683e-02  1.00689337e-01
 -9.55368646e-02 -2.56649293e-02  4.28368248e-02  3.75026751e-02
  4.04345379e-02  2.22588195e-02  3.52863981e-02  5.89132907e-02
  3.26950926e-02  4.74075081e-02 -1.14815317e-01 -1.55453727e-03
  1.37795730e-02 -6.91565660e-02 -7.95993613e-03  0.00000000e+00
 -8.17171042e-02 -1.11600993e-02  1.57703160e-02  1.78419276e-02
  8.16030736e-03 -2.48306616e-02  4.42584670e-02 -1.30252071e-01
 -5.88343244e-02 -1.58892100e-02 -5.42080053e-02  1.71380150e-02
 -5.09646932e-02 -1.05599734e-01  2.75380007e-02 -1.40944262e-02
 -9.73651202e-02 -1.59865901e-02 -1.10146820e-02  6.33472307e-02
  7.74479792e-03  5.89480012e-03 -4.50812495e-02  4.73876814e-02
 -1.21766663e-02  7.71214424e-03 -1.32726770e-02  3.26718518e-02
 -4.36980917e-02  2.88629869e-02  5.45491013e-03 -2.24386138e-02
 -7.28697945e-02 -4.03179678e-02  9.07835731e-02 -1.68990979e-02
  1.71899288e-02 -4.77063184e-02  1.27059745e-03 -2.57920202e-02
 -1.63909634e-02  2.29477449e-02  1.65424440e-02  2.16885913e-02
  4.41563747e-02 -6.80328074e-02  5.56196441e-02 -4.61927587e-02
  1.61951761e-02  3.92251798e-02  6.80366576e-03 -1.13954290e-02
  6.68218962e-02 -5.34367797e-03  2.32950731e-02  4.86120030e-02
  1.54677115e-02  7.55918308e-04  3.19998331e-02  7.17515737e-02
 -1.25622983e-02  9.55381868e-02 -7.18279690e-03  1.95675110e-02
  7.33179894e-02  5.45935144e-02 -1.39429114e-03  4.07752164e-03
 -1.40577777e-02 -6.17237749e-02 -1.22461592e-02 -1.39429114e-03
 -2.72061593e-02 -4.34033387e-02  1.47448912e-03 -3.48103003e-02
 -1.39429114e-03  4.97436161e-03 -3.70665374e-03 -3.13418631e-02
  4.66375191e-02 -7.25652339e-02  1.07525327e-01  3.41196635e-02
 -1.31332952e-02  8.92314351e-03 -1.19902497e-02  1.17185503e-03
  6.28803932e-02 -5.64693104e-02  4.72708846e-02 -5.47880966e-02
  2.47670396e-03  1.68471251e-03  1.78106762e-02  1.90685644e-03
  1.36692661e-02  1.26377550e-02  2.57177695e-02  8.04985869e-03
  1.63446731e-02  1.30913733e-02  4.45865264e-03 -8.51830678e-03
 -1.42621583e-02 -3.20364232e-02 -1.99569594e-02  3.67434198e-02
 -2.47031187e-03  4.57399642e-02 -4.16061553e-02 -2.88139929e-02
  9.35856346e-02  8.82376288e-02 -3.97731081e-02 -2.37815330e-03
  7.47353611e-03  3.31284294e-03  6.93317571e-02 -3.81155498e-02]
In [58]:
train_results = pd.DataFrame(y_train)
train_results['Model_Output(Log)'] = model.predict(X_train)
print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(train_results['LogSalePrice'], train_results['Model_Output(Log)'])))
Root Mean Squared Error: 0.07603728133760505
In [59]:
train_results.head()
Out[59]:
LogSalePrice Model_Output(Log)
1043 11.349229 11.430122
481 11.898188 11.859816
886 11.947949 11.928537
54 11.775290 11.733689
968 12.028739 12.091075
In [60]:
px.scatter(train_results,x='Model_Output(Log)',y='LogSalePrice',title='Multivariate Regression Training Predictions')

Testing the model on my validation set:

In [61]:
val_results = pd.DataFrame(y_val)
val_results['Model_Predictions(Log)'] = model.predict(X_val)
print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(val_results['LogSalePrice'], val_results['Model_Predictions(Log)'])))
Root Mean Squared Error: 0.1259781162779618
In [62]:
px.scatter(val_results,x='Model_Predictions(Log)',y='LogSalePrice',title='Multivariate Regression Validation Predictions')
In [63]:
val_results
Out[63]:
LogSalePrice Model_Predictions(Log)
1036 12.185870 12.176597
1124 11.813030 12.103738
997 11.827043 11.919396
1316 11.320554 11.545763
529 12.089539 12.119511
... ... ...
514 12.259613 12.277315
722 11.608236 12.073765
841 11.801857 11.755502
1079 11.898188 11.928691
1377 11.561716 11.531173

363 rows × 2 columns

Result

An Improvement of a 0.28935 RMSE to a 0.13298 RMSE. This pushed me up over 2400 places, into position 1610. Next, I think experimenting with the alpha parameter in Ridge Regression will be fruitful.

Model 4: Adjusting the Alpha Parameter in Ridge Regression

In [64]:
alpha_vals = [0.01,0.02,0.04,0.08,0.16,0.32,0.64,1.28,2.56,5.12,10.24,20.48,40.96,81.92,163.84,327.68,655.36,1310,2621,5242,10485]
train_errors = []
validation_errors = []
In [65]:
for a in alpha_vals:
    model = Ridge(alpha=a, fit_intercept=True);
    model.fit(X_train, y_train); # Fit the model to the training data
    
    train_results = pd.DataFrame(y_train)
    train_results['Model_Output(Log)'] = model.predict(X_train)
    train_errors.append(np.sqrt(metrics.mean_squared_error(train_results['LogSalePrice'], train_results['Model_Output(Log)'])))
    #px.scatter(train_results,x='Model_Output(Log)',y='LogSalePrice',title='Train Output: Alpha = {}'.format(a))

    val_results = pd.DataFrame(y_val)
    val_results['Model_Predictions(Log)'] = model.predict(X_val)
    validation_errors.append(np.sqrt(metrics.mean_squared_error(val_results['LogSalePrice'], val_results['Model_Predictions(Log)'])))
    #px.scatter(val_results,x='Model_Predictions(Log)',y='LogSalePrice',title='Validation Output: Alpha = {}'.format(a))
Out[65]:
Ridge(alpha=0.01, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=0.02, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=0.04, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=0.08, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=0.16, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=0.32, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=0.64, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=1.28, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=2.56, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=5.12, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=10.24, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=20.48, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=40.96, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=81.92, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=163.84, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=327.68, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=655.36, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=1310, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=2621, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=5242, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
Out[65]:
Ridge(alpha=10485, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)
In [66]:
alpha_results = pd.DataFrame(data = {'Alpha': alpha_vals, 'Training_Errors': train_errors, 'Validation_Errors': validation_errors})
alpha_results
Out[66]:
Alpha Training_Errors Validation_Errors
0 0.01 0.067638 0.158029
1 0.02 0.067900 0.154480
2 0.04 0.068310 0.150081
3 0.08 0.068958 0.144893
4 0.16 0.070011 0.139286
5 0.32 0.071664 0.133808
6 0.64 0.074068 0.128850
7 1.28 0.077259 0.124486
8 2.56 0.081099 0.120626
9 5.12 0.085350 0.117299
10 10.24 0.089893 0.114786
11 20.48 0.094800 0.113502
12 40.96 0.100217 0.113801
13 81.92 0.106172 0.115865
14 163.84 0.112611 0.119703
15 327.68 0.119816 0.125356
16 655.36 0.128788 0.133197
17 1310.00 0.140655 0.143726
18 2621.00 0.154777 0.156220
19 5242.00 0.168191 0.168116
20 10485.00 0.178345 0.177166
In [67]:
fig = go.Figure(data=go.Scatter(
                x=alpha_results['Alpha'],
                y=alpha_results['Training_Errors'],
                mode='lines+markers',
                name = 'Training Error',
                hovertemplate='Alpha: %{x} <br>Log RMSE: %{y} '
));

fig.add_trace(go.Scatter(
                x=alpha_results['Alpha'],
                y=alpha_results['Validation_Errors'],
                mode='lines+markers',
                name = 'Validation Error',
                hovertemplate='Alpha: %{x} <br>Log RMSE: %{y} '
));

fig.update_layout(
    title='Impact of Regularisation Parameter on Log RMSE of Training and Validation Sets',
    xaxis_title='Regularisation Parameter, Alpha',
    yaxis_title='Log RMSE'
)

It is favourable to reduce the Validation Error, since this best emulates the Test Set. I now, apply a Ridge Model with alpha parameter set to 20 to predict house prices in my test set.

In [68]:
model = Ridge(alpha=20, fit_intercept=True)
model.fit(X_train, y_train) # Fit the model to the training data
print('Model Intercept:',round(model.intercept_,2))
print('Model Coefficients:', model.coef_)
Out[68]:
Ridge(alpha=20, copy_X=True, fit_intercept=True, max_iter=None, normalize=False,
      random_state=None, solver='auto', tol=0.001)
Model Intercept: 10.44
Model Coefficients: [ 5.11783709e-04  4.05126770e-06  5.03915118e-02  4.59720532e-02
  2.14961870e-05  7.49667016e-05  4.20016860e-05 -3.32440026e-06
  1.13643988e-04  8.70777167e-05  8.89350560e-05 -3.87040153e-05
  1.37308759e-04  1.82232476e-02 -4.82936574e-03  2.81762060e-02
  2.86405668e-02 -7.74610088e-03 -4.41679412e-02  7.92422007e-03
  1.43416232e-02  2.74555392e-02  9.52209940e-05  1.04149758e-04
  8.57104979e-05  2.23958323e-05  2.03766620e-04  1.97260757e-04
  1.08352841e-04 -4.46591736e-06  0.00000000e+00 -2.22873800e-02
 -4.85582490e-03 -1.61255448e-02  1.25247118e-02 -5.30364192e-02
  8.86232369e-03 -1.67241675e-03 -3.45827817e-03  1.04643428e-02
  1.91051764e-02  5.47253301e-03  6.32760662e-03  8.61451974e-03
  7.97679221e-03  3.77629603e-02  2.71888281e-02  3.53124154e-02
 -9.30356120e-03  1.62214738e-02 -1.11769174e-02  1.70968349e-02
  1.38487124e-02  8.21159736e-04  3.13006963e-03  1.56431278e-02
 -6.73660636e-03  9.30690889e-03 -5.86327701e-03  2.82996798e-02
 -2.06076406e-02 -4.20765782e-03 -5.64903463e-03  1.41305318e-03
 -2.10936853e-02 -2.07600636e-03 -1.79162421e-03  2.36239513e-02
  1.38972746e-02 -4.18631731e-03  6.11567341e-02 -2.83221403e-02
 -2.93506663e-03 -3.83571404e-02 -2.92555753e-02 -1.09638247e-02
 -1.42427221e-02  6.88644753e-03 -1.77103499e-02  3.98456068e-03
  3.41166604e-02 -3.80258592e-02 -1.02513854e-02 -1.18512816e-02
  1.11362985e-03  2.70780910e-02  4.73415262e-02 -1.74276809e-03
  4.34462041e-03  1.41409260e-02  4.36223103e-02 -5.21925445e-03
  1.13206438e-02 -2.17147615e-02  5.29329106e-03  2.40206791e-03
  7.84080190e-03  6.16603222e-03  9.95040363e-03  5.69864132e-04
 -5.55940365e-03 -2.95191333e-03  0.00000000e+00  0.00000000e+00
 -1.36155204e-02  7.97679221e-03 -1.35838304e-02  7.89778324e-03
 -4.90121155e-03 -3.77028050e-03 -5.66870307e-03  4.29484770e-03
 -9.33785163e-03 -2.20708390e-03  1.69782889e-02  0.00000000e+00
  0.00000000e+00 -1.29913486e-03 -4.95360108e-03  5.80390604e-04
 -8.54656783e-03  1.97604901e-03  5.69864132e-04  0.00000000e+00
  0.00000000e+00 -6.15879668e-03 -2.06544750e-02  0.00000000e+00
  0.00000000e+00  9.64327044e-04  5.26416112e-03  5.49302903e-04
  0.00000000e+00 -2.68993999e-03 -2.20303489e-02  3.49006391e-03
  1.55791424e-03 -4.51097861e-03 -3.65913870e-03  1.65103007e-03
  9.83441986e-03  0.00000000e+00 -1.02040697e-02  1.96590179e-03
 -3.87571943e-02  1.11799986e-02 -7.22979687e-03  1.88311570e-02
 -1.37293841e-02 -8.24730747e-03 -1.15999880e-02 -1.10779877e-02
  9.52885242e-03  6.24494784e-03 -8.76753408e-03 -2.13994172e-03
  1.63813864e-02  9.78908982e-03  1.36051327e-03  1.17546564e-02
 -2.88464710e-03 -2.56837430e-03 -3.33682439e-03  3.79862375e-03
 -1.94539805e-02 -8.97743103e-05  5.12995787e-03 -6.06907722e-03
  1.13829278e-03  2.93841884e-03 -5.91353088e-03  5.07929590e-03
  7.65852196e-03 -1.66429790e-03  3.10367149e-04  1.07458247e-02
  7.06047889e-03 -1.26602660e-03 -3.19401619e-03  1.01634513e-02
 -2.53879357e-03  1.36706291e-02  9.20775770e-04  1.02677684e-02
 -8.78289856e-03 -1.17004869e-02 -1.43113201e-02 -1.71065397e-04
 -1.08880305e-03 -1.02060524e-02 -4.71114033e-03 -3.73516154e-03
  5.03952326e-03 -1.30804708e-02 -1.60920318e-02  1.07440814e-02
 -2.01494003e-03 -1.69333514e-02 -4.32078108e-03  1.10044499e-04
  5.67343941e-03  6.83618073e-03 -8.96530066e-03  7.77566133e-03
  9.24160455e-05 -6.00086569e-03  4.90709791e-03  5.36305270e-03
  1.64757657e-02 -6.80509736e-03  5.31680142e-03 -6.04652691e-03
 -1.27468204e-03 -8.70562040e-03 -5.63771305e-03 -2.94744263e-03
  1.21676776e-02  1.22766940e-02  5.40027361e-03  7.71167467e-03
  3.42068153e-03  2.16863472e-03  3.78805141e-03 -4.77095728e-03
 -3.76739034e-03 -1.69155002e-03  1.59676894e-02 -4.26608354e-03
  2.32493944e-02  3.71813515e-02  1.65397978e-02  9.63723777e-03
  6.02020330e-03 -1.66429790e-03 -5.56513416e-03  4.27235175e-04
  1.70334645e-02 -8.45206053e-03  1.14441090e-03 -6.44523115e-03
 -6.67977186e-03  3.60284025e-03  6.02410360e-03  2.07190410e-02
 -1.12335486e-02 -5.60996800e-04 -1.52062828e-02  1.10523658e-02
  5.69678691e-06  6.43581595e-03 -9.18104470e-03  2.98466176e-03
  3.70526534e-03 -8.61132090e-03 -1.22462221e-02  4.13610439e-03
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  3.28506213e-03  4.00478159e-03  1.92748830e-04  1.66020511e-03
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  8.29367447e-03  5.23941904e-03  1.21293341e-02  1.98541495e-03
  5.01384032e-03  1.55037926e-02  1.81609022e-02  6.67033501e-03
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  6.37607058e-04  0.00000000e+00  3.97176198e-03 -2.65570104e-03
 -8.23933441e-03  3.85236383e-03  2.11224708e-03  0.00000000e+00
 -1.53884372e-02  4.13328558e-02 -3.54142347e-03  4.25939980e-03
 -1.14004225e-03  0.00000000e+00  6.76516449e-03  2.00940221e-04
  4.14858955e-03 -1.70378259e-03  1.89174706e-02 -3.24636952e-02
  7.98355681e-03  5.33500470e-03 -5.61745779e-03  4.31376605e-03
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  2.46801953e-03 -1.70333315e-03  2.87807429e-03 -9.03632567e-04
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  5.98139695e-04 -4.15040627e-04  1.69111115e-02 -1.01126809e-02
 -5.36765283e-03 -2.15393020e-02  6.59328736e-03 -1.39483101e-02
  1.41545315e-03  3.70515171e-03 -3.81066071e-03  3.93492339e-02
  3.85254190e-03 -4.04442143e-03 -1.04053479e-02 -1.59885333e-02
 -1.58140865e-02  1.94237560e-03 -3.86244105e-02  1.32789506e-02
  1.94237560e-03  1.27981759e-03  2.00546438e-02  3.02126060e-02
  1.12747713e-03 -4.95100427e-03  1.94237560e-03  4.71508204e-03
  9.27844051e-03 -7.11112923e-03  1.94237560e-03 -1.92003496e-02
 -1.31841947e-02 -2.09387286e-02  9.74613042e-03 -7.04984038e-04
 -2.79484534e-03 -3.57584779e-03  1.36303445e-02  2.15376392e-02
  1.08785192e-03 -8.75231055e-03 -6.93639356e-03 -6.57453064e-04
 -8.49111619e-03 -2.21462155e-02 -1.93242596e-03 -2.50380851e-02
  6.00437979e-02  6.97211603e-03 -2.47984815e-03 -1.87655506e-03
  1.02983574e-03 -1.90711336e-02 -1.95413798e-02 -2.71264573e-02
 -1.37725356e-02  3.09788052e-03  1.33218465e-02 -3.23474647e-02
  0.00000000e+00  5.31170352e-02 -6.47397284e-03  6.84453885e-03
 -8.52361298e-03  6.20113096e-05 -6.48634935e-03  2.08524503e-02
 -1.54114045e-02  2.06124572e-02 -1.23396554e-02  2.93466970e-03
 -2.91536385e-03  0.00000000e+00 -9.09415049e-03  5.49302903e-04
 -2.68993999e-03 -8.31154557e-04  1.23840350e-03 -6.26635225e-03
 -7.16365632e-03  0.00000000e+00 -8.12398706e-03  0.00000000e+00
 -2.04349777e-03  9.32851051e-03  1.30644367e-02  1.04245325e-02
 -1.24278170e-02 -1.15740193e-02  2.30295991e-03  6.10627862e-03
 -9.49829360e-03  1.84287967e-03  7.96973320e-03  3.87798232e-03
  6.45585070e-03  1.25834442e-03  6.32667610e-03  9.60262293e-03
  7.25529023e-03  4.90694440e-03 -1.30204581e-02  1.24051260e-03
  1.22058496e-02 -1.88383823e-02 -8.97743103e-05  0.00000000e+00
 -1.00935841e-02 -3.32626138e-03  1.52670639e-03  2.05756445e-03
  3.84974819e-03  2.50511892e-03  8.15197357e-03 -1.90204329e-02
 -1.25476447e-02  3.58912604e-03 -8.12187760e-03  9.00352049e-04
 -6.46303319e-03 -2.22986911e-02 -1.51498627e-04  7.74824582e-03
 -1.56037072e-02  9.87333608e-03 -6.41613364e-03  8.79544821e-03
 -1.38100733e-02  4.33709178e-03 -1.31523893e-02  6.29499301e-03
 -8.23505092e-03 -4.29893284e-03 -3.67593550e-03  4.55077344e-03
 -1.60920318e-02  1.98521353e-02 -8.46608076e-03 -1.11124231e-02
 -2.39485750e-02 -1.29700045e-02  1.66095458e-02 -5.66962348e-03
 -5.82031800e-04 -5.33314641e-03  2.95124749e-03 -6.91120950e-03
 -3.64845170e-03  4.92152154e-03  1.02099963e-02 -1.64410289e-03
  5.47232468e-03 -1.71744807e-02  1.36439397e-02 -1.16021402e-02
  8.16649198e-04 -3.29756457e-03  5.40195578e-03 -1.08103988e-03
  1.54819049e-02  3.86683214e-03  4.48921595e-03  1.62985426e-02
  3.78805141e-03 -5.73406094e-03  7.54714399e-03  3.36200497e-03
  6.56519480e-04  2.10570909e-02 -2.92166161e-03  1.96767892e-02
  3.04879065e-02  1.03364515e-02 -2.91536385e-03 -6.01557620e-03
 -1.14136138e-02 -1.35061545e-02  1.01438991e-02 -2.91536385e-03
 -2.76520619e-03 -3.59509087e-03 -7.58939167e-03  7.68972760e-04
 -2.91536385e-03 -3.21333185e-03  8.58726077e-03 -8.78919025e-03
  3.88753481e-02 -8.73187136e-03  1.30745982e-02  3.96316488e-03
 -4.76887427e-03  5.54877547e-03 -1.77573859e-03  6.69379078e-03
  1.42709533e-02 -7.50032958e-03  6.35248285e-04 -8.49943264e-03
 -5.19252660e-03 -1.22286322e-02  6.39258340e-03 -2.06318465e-03
  1.89925161e-03 -1.82232400e-03  1.35336067e-02  3.04191975e-03
  9.96180925e-03  9.99255458e-03 -7.15105533e-03  1.32582332e-03
 -6.39315307e-03 -1.92498015e-02 -1.00313979e-02  7.53602693e-03
  1.86443723e-03  1.42867345e-02 -8.88347625e-03 -4.98687787e-03
  4.23295806e-02  1.50518749e-02 -2.57635244e-02 -1.34934221e-03
 -3.47651781e-04 -7.86265025e-03  5.31090704e-02  2.53096886e-02]

Result

An Improvement of a 0.13298 RMSE to a 0.12540 RMSE. This pushed me up over 500 places, into position 1096.

Model 5: Lasso Regularised Regression

Lasso uses L1 penalties (Sum of the coefficients)

In [69]:
alpha_vals = [0.0001,0.00025,0.0005,0.0007,0.001,0.0025,0.005,0.01,0.02]
train_errors = []
validation_errors = []
In [70]:
for a in alpha_vals:
    model = Lasso(alpha=a, fit_intercept=True);
    model.fit(X_train, y_train); # Fit the model to the training data
    
    train_results = pd.DataFrame(y_train)
    train_results['Model_Output(Log)'] = model.predict(X_train)
    train_errors.append(np.sqrt(metrics.mean_squared_error(train_results['LogSalePrice'], train_results['Model_Output(Log)'])))
    #px.scatter(train_results,x='Model_Output(Log)',y='LogSalePrice',title='Train Output: Alpha = {}'.format(a))

    val_results = pd.DataFrame(y_val)
    val_results['Model_Predictions(Log)'] = model.predict(X_val)
    validation_errors.append(np.sqrt(metrics.mean_squared_error(val_results['LogSalePrice'], val_results['Model_Predictions(Log)'])))
    #px.scatter(val_results,x='Model_Predictions(Log)',y='LogSalePrice',title='Validation Output: Alpha = {}'.format(a))
Out[70]:
Lasso(alpha=0.0001, copy_X=True, fit_intercept=True, max_iter=1000,
      normalize=False, positive=False, precompute=False, random_state=None,
      selection='cyclic', tol=0.0001, warm_start=False)
Out[70]:
Lasso(alpha=0.00025, copy_X=True, fit_intercept=True, max_iter=1000,
      normalize=False, positive=False, precompute=False, random_state=None,
      selection='cyclic', tol=0.0001, warm_start=False)
Out[70]:
Lasso(alpha=0.0005, copy_X=True, fit_intercept=True, max_iter=1000,
      normalize=False, positive=False, precompute=False, random_state=None,
      selection='cyclic', tol=0.0001, warm_start=False)
Out[70]:
Lasso(alpha=0.0007, copy_X=True, fit_intercept=True, max_iter=1000,
      normalize=False, positive=False, precompute=False, random_state=None,
      selection='cyclic', tol=0.0001, warm_start=False)
Out[70]:
Lasso(alpha=0.001, copy_X=True, fit_intercept=True, max_iter=1000,
      normalize=False, positive=False, precompute=False, random_state=None,
      selection='cyclic', tol=0.0001, warm_start=False)
Out[70]:
Lasso(alpha=0.0025, copy_X=True, fit_intercept=True, max_iter=1000,
      normalize=False, positive=False, precompute=False, random_state=None,
      selection='cyclic', tol=0.0001, warm_start=False)
Out[70]:
Lasso(alpha=0.005, copy_X=True, fit_intercept=True, max_iter=1000,
      normalize=False, positive=False, precompute=False, random_state=None,
      selection='cyclic', tol=0.0001, warm_start=False)
Out[70]:
Lasso(alpha=0.01, copy_X=True, fit_intercept=True, max_iter=1000,
      normalize=False, positive=False, precompute=False, random_state=None,
      selection='cyclic', tol=0.0001, warm_start=False)
Out[70]:
Lasso(alpha=0.02, copy_X=True, fit_intercept=True, max_iter=1000,
      normalize=False, positive=False, precompute=False, random_state=None,
      selection='cyclic', tol=0.0001, warm_start=False)
In [71]:
alpha_results = pd.DataFrame(data = {'Alpha': alpha_vals, 'Training_Errors': train_errors, 'Validation_Errors': validation_errors})
alpha_results
Out[71]:
Alpha Training_Errors Validation_Errors
0 0.00010 0.080746 0.119756
1 0.00025 0.091350 0.115464
2 0.00050 0.099312 0.114730
3 0.00070 0.102318 0.114789
4 0.00100 0.105630 0.114773
5 0.00250 0.116732 0.120109
6 0.00500 0.126395 0.127217
7 0.01000 0.138529 0.137425
8 0.02000 0.150356 0.146651
In [72]:
fig = go.Figure(data=go.Scatter(
                x=alpha_results['Alpha'],
                y=alpha_results['Training_Errors'],
                mode='lines+markers',
                name = 'Training Error',
                hovertemplate='Alpha: %{x} <br>Log RMSE: %{y} '
));

fig.add_trace(go.Scatter(
                x=alpha_results['Alpha'],
                y=alpha_results['Validation_Errors'],
                mode='lines+markers',
                name = 'Validation Error',
                hovertemplate='Alpha: %{x} <br>Log RMSE: %{y} '
));

fig.update_layout(
    title='Impact of Regularisation Parameter on Log RMSE of Training and Validation Sets',
    xaxis_title='Regularisation Parameter, Alpha',
    yaxis_title='Log RMSE'
)

We see that the validation set error is minimised with alpha set to around 0.0005. I apply this model below and submit.

In [73]:
model = Lasso(alpha=0.0005, fit_intercept=True)
model.fit(X_train, y_train) # Fit the model to the training data
print('Model Intercept:',round(model.intercept_,2))
print('Model Coefficients:', model.coef_)
Out[73]:
Lasso(alpha=0.0005, copy_X=True, fit_intercept=True, max_iter=1000,
      normalize=False, positive=False, precompute=False, random_state=None,
      selection='cyclic', tol=0.0001, warm_start=False)
Model Intercept: 10.43
Model Coefficients: [ 5.26930614e-04  4.12858108e-06  5.08305982e-02  4.51149463e-02
  3.14599619e-05  1.38559752e-04  1.02087831e-04  5.80112838e-05
  3.85175493e-05  2.12816795e-04  1.92705587e-04  6.72155313e-05
  2.97032880e-05  1.86357213e-02 -0.00000000e+00  2.86704855e-02
  2.74007487e-02 -7.38834611e-03 -6.76054410e-02  7.70657391e-03
  1.32254757e-02  3.13284854e-02  8.89037998e-05  1.07953034e-04
  1.12087354e-04  7.05058597e-06  1.66125054e-04  1.72830148e-04
  1.20688753e-04 -3.12736891e-06  0.00000000e+00 -3.16983219e-02
 -0.00000000e+00 -1.60006471e-02 -0.00000000e+00 -7.60918233e-02
  0.00000000e+00 -0.00000000e+00 -2.38145038e-03  0.00000000e+00
  0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00
  0.00000000e+00  6.10599712e-02  4.86259035e-02  4.56367278e-02
  0.00000000e+00  0.00000000e+00 -1.14309805e-05  1.80608884e-02
  4.31703354e-03  0.00000000e+00 -0.00000000e+00  0.00000000e+00
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 -3.86995838e-03 -0.00000000e+00 -0.00000000e+00  1.59096256e-02
 -3.64160678e-03  1.67424802e-02 -0.00000000e+00  0.00000000e+00
 -0.00000000e+00  0.00000000e+00 -0.00000000e+00  0.00000000e+00
 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00
 -0.00000000e+00  0.00000000e+00 -0.00000000e+00  0.00000000e+00
 -0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00
 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00  0.00000000e+00
 -0.00000000e+00 -0.00000000e+00  0.00000000e+00  0.00000000e+00
  0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00
  0.00000000e+00  0.00000000e+00 -0.00000000e+00  0.00000000e+00
  0.00000000e+00 -1.73323009e-03  0.00000000e+00  0.00000000e+00
 -0.00000000e+00 -0.00000000e+00  0.00000000e+00  0.00000000e+00
  0.00000000e+00  0.00000000e+00  0.00000000e+00 -0.00000000e+00
 -0.00000000e+00  0.00000000e+00 -0.00000000e+00 -0.00000000e+00
 -0.00000000e+00 -2.81391711e-03 -0.00000000e+00  0.00000000e+00
 -0.00000000e+00  0.00000000e+00 -0.00000000e+00  0.00000000e+00
 -1.50216497e-02  0.00000000e+00 -0.00000000e+00  0.00000000e+00
 -0.00000000e+00 -0.00000000e+00  0.00000000e+00  0.00000000e+00
 -1.26034441e-04  1.32100683e-02 -0.00000000e+00 -0.00000000e+00
 -2.23562908e-02 -0.00000000e+00  2.27541687e-03 -0.00000000e+00
 -0.00000000e+00 -0.00000000e+00  0.00000000e+00 -0.00000000e+00
 -0.00000000e+00  0.00000000e+00  0.00000000e+00 -0.00000000e+00
  0.00000000e+00 -0.00000000e+00  0.00000000e+00 -0.00000000e+00
 -0.00000000e+00 -0.00000000e+00  0.00000000e+00  0.00000000e+00
  6.42357299e-03  0.00000000e+00  0.00000000e+00  0.00000000e+00
  0.00000000e+00 -0.00000000e+00  0.00000000e+00 -0.00000000e+00
  0.00000000e+00  3.47114370e-03 -0.00000000e+00  3.67204319e-03
  4.83804360e-02  0.00000000e+00 -0.00000000e+00 -1.59466805e-03
 -3.37633886e-03 -5.86075732e-03  0.00000000e+00 -0.00000000e+00
 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00  0.00000000e+00
 -0.00000000e+00 -0.00000000e+00  0.00000000e+00 -0.00000000e+00
  4.03875935e-02 -0.00000000e+00  0.00000000e+00  0.00000000e+00
 -0.00000000e+00  0.00000000e+00 -0.00000000e+00  2.21104476e-03
  7.89769946e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00
 -1.01669137e-03 -6.77040533e-03  0.00000000e+00 -0.00000000e+00
 -0.00000000e+00 -0.00000000e+00  8.82178342e-03  0.00000000e+00
  7.19799137e-03  4.07046653e-03 -0.00000000e+00  0.00000000e+00
 -0.00000000e+00 -1.48296789e-02 -3.52924818e-03  0.00000000e+00
  0.00000000e+00  0.00000000e+00 -0.00000000e+00 -0.00000000e+00
  8.73118720e-02  0.00000000e+00 -2.33513558e-02  0.00000000e+00
  0.00000000e+00 -0.00000000e+00  6.26754553e-02  0.00000000e+00]

Result

An Improvement of a 0.12540 RMSE to a 0.12502 RMSE. This pushed me up 28 places, into position 1051.

Model 6: Elastic Net Regularised Regression

Elastic Net takes a combination of L1 and L2 penalties. It has hyperparameters, alpha (as before) and

In [74]:
alpha_vals = [0.0001,0.00025,0.0005,0.0007,0.001,0.0025,0.005,0.01,0.02,0.04,0.1]
l1_ratios = [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9]
train_errors = []
validation_errors = []
alpha_order = []
ratio_order = []
In [75]:
for a in alpha_vals:
        for r in l1_ratios:
            alpha_order.append(a)
            ratio_order.append(r)
            model =ElasticNet(alpha=a, l1_ratio=r, fit_intercept=True, normalize=False)
            model.fit(X_train, y_train); # Fit the model to the training data

            train_results = pd.DataFrame(y_train)
            train_results['Model_Output(Log)'] = model.predict(X_train)
            train_errors.append(np.sqrt(metrics.mean_squared_error(train_results['LogSalePrice'], train_results['Model_Output(Log)'])))
            #px.scatter(train_results,x='Model_Output(Log)',y='LogSalePrice',title='Train Output: Alpha = {}'.format(a))

            val_results = pd.DataFrame(y_val)
            val_results['Model_Predictions(Log)'] = model.predict(X_val)
            validation_errors.append(np.sqrt(metrics.mean_squared_error(val_results['LogSalePrice'], val_results['Model_Predictions(Log)'])))
            #px.scatter(val_results,x='Model_Predictions(Log)',y='LogSalePrice',title='Validation Output: Alpha = {}'.format(a))
Out[75]:
ElasticNet(alpha=0.0001, copy_X=True, fit_intercept=True, l1_ratio=0.1,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0001, copy_X=True, fit_intercept=True, l1_ratio=0.2,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0001, copy_X=True, fit_intercept=True, l1_ratio=0.3,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0001, copy_X=True, fit_intercept=True, l1_ratio=0.4,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0001, copy_X=True, fit_intercept=True, l1_ratio=0.5,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0001, copy_X=True, fit_intercept=True, l1_ratio=0.6,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0001, copy_X=True, fit_intercept=True, l1_ratio=0.7,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0001, copy_X=True, fit_intercept=True, l1_ratio=0.8,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0001, copy_X=True, fit_intercept=True, l1_ratio=0.9,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.00025, copy_X=True, fit_intercept=True, l1_ratio=0.1,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.00025, copy_X=True, fit_intercept=True, l1_ratio=0.2,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.00025, copy_X=True, fit_intercept=True, l1_ratio=0.3,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.00025, copy_X=True, fit_intercept=True, l1_ratio=0.4,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.00025, copy_X=True, fit_intercept=True, l1_ratio=0.5,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.00025, copy_X=True, fit_intercept=True, l1_ratio=0.6,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.00025, copy_X=True, fit_intercept=True, l1_ratio=0.7,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.00025, copy_X=True, fit_intercept=True, l1_ratio=0.8,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.00025, copy_X=True, fit_intercept=True, l1_ratio=0.9,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0005, copy_X=True, fit_intercept=True, l1_ratio=0.1,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0005, copy_X=True, fit_intercept=True, l1_ratio=0.2,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0005, copy_X=True, fit_intercept=True, l1_ratio=0.3,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0005, copy_X=True, fit_intercept=True, l1_ratio=0.4,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0005, copy_X=True, fit_intercept=True, l1_ratio=0.5,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0005, copy_X=True, fit_intercept=True, l1_ratio=0.6,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0005, copy_X=True, fit_intercept=True, l1_ratio=0.7,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0005, copy_X=True, fit_intercept=True, l1_ratio=0.8,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0005, copy_X=True, fit_intercept=True, l1_ratio=0.9,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0007, copy_X=True, fit_intercept=True, l1_ratio=0.1,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0007, copy_X=True, fit_intercept=True, l1_ratio=0.2,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0007, copy_X=True, fit_intercept=True, l1_ratio=0.3,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0007, copy_X=True, fit_intercept=True, l1_ratio=0.4,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0007, copy_X=True, fit_intercept=True, l1_ratio=0.5,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0007, copy_X=True, fit_intercept=True, l1_ratio=0.6,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0007, copy_X=True, fit_intercept=True, l1_ratio=0.7,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0007, copy_X=True, fit_intercept=True, l1_ratio=0.8,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0007, copy_X=True, fit_intercept=True, l1_ratio=0.9,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.001, copy_X=True, fit_intercept=True, l1_ratio=0.1,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.001, copy_X=True, fit_intercept=True, l1_ratio=0.2,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.001, copy_X=True, fit_intercept=True, l1_ratio=0.3,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.001, copy_X=True, fit_intercept=True, l1_ratio=0.4,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.001, copy_X=True, fit_intercept=True, l1_ratio=0.5,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.001, copy_X=True, fit_intercept=True, l1_ratio=0.6,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.001, copy_X=True, fit_intercept=True, l1_ratio=0.7,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.001, copy_X=True, fit_intercept=True, l1_ratio=0.8,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.001, copy_X=True, fit_intercept=True, l1_ratio=0.9,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0025, copy_X=True, fit_intercept=True, l1_ratio=0.1,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0025, copy_X=True, fit_intercept=True, l1_ratio=0.2,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0025, copy_X=True, fit_intercept=True, l1_ratio=0.3,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0025, copy_X=True, fit_intercept=True, l1_ratio=0.4,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0025, copy_X=True, fit_intercept=True, l1_ratio=0.5,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0025, copy_X=True, fit_intercept=True, l1_ratio=0.6,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0025, copy_X=True, fit_intercept=True, l1_ratio=0.7,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0025, copy_X=True, fit_intercept=True, l1_ratio=0.8,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.0025, copy_X=True, fit_intercept=True, l1_ratio=0.9,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.005, copy_X=True, fit_intercept=True, l1_ratio=0.1,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.005, copy_X=True, fit_intercept=True, l1_ratio=0.2,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.005, copy_X=True, fit_intercept=True, l1_ratio=0.3,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.005, copy_X=True, fit_intercept=True, l1_ratio=0.4,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.005, copy_X=True, fit_intercept=True, l1_ratio=0.5,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.005, copy_X=True, fit_intercept=True, l1_ratio=0.6,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.005, copy_X=True, fit_intercept=True, l1_ratio=0.7,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.005, copy_X=True, fit_intercept=True, l1_ratio=0.8,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.005, copy_X=True, fit_intercept=True, l1_ratio=0.9,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.01, copy_X=True, fit_intercept=True, l1_ratio=0.1,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.01, copy_X=True, fit_intercept=True, l1_ratio=0.2,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.01, copy_X=True, fit_intercept=True, l1_ratio=0.3,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.01, copy_X=True, fit_intercept=True, l1_ratio=0.4,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.01, copy_X=True, fit_intercept=True, l1_ratio=0.5,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.01, copy_X=True, fit_intercept=True, l1_ratio=0.6,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.01, copy_X=True, fit_intercept=True, l1_ratio=0.7,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.01, copy_X=True, fit_intercept=True, l1_ratio=0.8,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.01, copy_X=True, fit_intercept=True, l1_ratio=0.9,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.02, copy_X=True, fit_intercept=True, l1_ratio=0.1,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.02, copy_X=True, fit_intercept=True, l1_ratio=0.2,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.02, copy_X=True, fit_intercept=True, l1_ratio=0.3,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.02, copy_X=True, fit_intercept=True, l1_ratio=0.4,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.02, copy_X=True, fit_intercept=True, l1_ratio=0.5,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.02, copy_X=True, fit_intercept=True, l1_ratio=0.6,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.02, copy_X=True, fit_intercept=True, l1_ratio=0.7,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.02, copy_X=True, fit_intercept=True, l1_ratio=0.8,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.02, copy_X=True, fit_intercept=True, l1_ratio=0.9,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.04, copy_X=True, fit_intercept=True, l1_ratio=0.1,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.04, copy_X=True, fit_intercept=True, l1_ratio=0.2,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.04, copy_X=True, fit_intercept=True, l1_ratio=0.3,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.04, copy_X=True, fit_intercept=True, l1_ratio=0.4,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.04, copy_X=True, fit_intercept=True, l1_ratio=0.5,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.04, copy_X=True, fit_intercept=True, l1_ratio=0.6,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.04, copy_X=True, fit_intercept=True, l1_ratio=0.7,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.04, copy_X=True, fit_intercept=True, l1_ratio=0.8,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.04, copy_X=True, fit_intercept=True, l1_ratio=0.9,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.1, copy_X=True, fit_intercept=True, l1_ratio=0.1,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.1, copy_X=True, fit_intercept=True, l1_ratio=0.2,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.1, copy_X=True, fit_intercept=True, l1_ratio=0.3,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.1, copy_X=True, fit_intercept=True, l1_ratio=0.4,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.1, copy_X=True, fit_intercept=True, l1_ratio=0.5,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.1, copy_X=True, fit_intercept=True, l1_ratio=0.6,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.1, copy_X=True, fit_intercept=True, l1_ratio=0.7,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.1, copy_X=True, fit_intercept=True, l1_ratio=0.8,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Out[75]:
ElasticNet(alpha=0.1, copy_X=True, fit_intercept=True, l1_ratio=0.9,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
In [76]:
alpha_results = pd.DataFrame(data = {'Alpha': alpha_order, 'Ratio': ratio_order, 'Training_Errors': train_errors, 'Validation_Errors': validation_errors})
alpha_results.sort_values('Validation_Errors')
Out[76]:
Alpha Ratio Training_Errors Validation_Errors
54 0.0050 0.1 0.100781 0.114168
46 0.0025 0.2 0.099989 0.114393
40 0.0010 0.5 0.099487 0.114611
41 0.0010 0.6 0.101128 0.114618
34 0.0007 0.8 0.100416 0.114651
... ... ... ... ...
94 0.1000 0.5 0.162527 0.159087
95 0.1000 0.6 0.166182 0.162912
96 0.1000 0.7 0.170404 0.167303
97 0.1000 0.8 0.175191 0.172259
98 0.1000 0.9 0.180485 0.177693

99 rows × 4 columns

We see that the validation set error is minimised with alpha set to around 0.005. I apply this model below and submit.

In [77]:
model = ElasticNet(alpha=0.005,l1_ratio = 0.1, fit_intercept=True)
model.fit(X_train, y_train) # Fit the model to the training data
print('Model Intercept:',round(model.intercept_,2))
print('Model Coefficients:', model.coef_)
Out[77]:
ElasticNet(alpha=0.005, copy_X=True, fit_intercept=True, l1_ratio=0.1,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
Model Intercept: 10.44
Model Coefficients: [ 5.44812295e-04  4.15483358e-06  5.28208656e-02  4.54359226e-02
  3.10593134e-05  1.41140336e-04  1.02434725e-04  5.89001872e-05
  3.90207851e-05  2.12305214e-04  1.92555420e-04  6.63013783e-05
  2.96472976e-05  1.81470441e-02 -0.00000000e+00  2.63164907e-02
  2.70991956e-02 -8.43277237e-03 -5.82311487e-02  7.97980069e-03
  1.36540336e-02  2.92362760e-02  9.56005490e-05  1.04159106e-04
  1.10850386e-04  7.89672809e-06  1.75647259e-04  1.75032892e-04
  1.11609256e-04 -3.75364443e-06  0.00000000e+00 -2.62741267e-02
 -0.00000000e+00 -1.37417512e-02  0.00000000e+00 -6.58312604e-02
  0.00000000e+00 -0.00000000e+00 -0.00000000e+00  0.00000000e+00
  3.55712153e-03  0.00000000e+00  0.00000000e+00  0.00000000e+00
  0.00000000e+00  4.79914369e-02  2.60086435e-02  4.12758719e-02
 -0.00000000e+00  0.00000000e+00 -6.29835324e-05  1.83425083e-02
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  0.00000000e+00 -0.00000000e+00  5.61507488e-02  9.61649707e-03]

Result

No Improvement: This had an RMSE of 0.12523.

Submission Export

This code takes the most recently defined model and outputs the predictions to csv.

In [79]:
# Reset the test data frame, and make predictions based on the latest defined model.
test['Log_Predictions'] = model.predict(test.drop(['Id','Predictions','Log_Predictions'],axis=1)) 
test['Predictions'] = np.exp(test['Log_Predictions']) # Take the exponential of my predictions ready for submission

#test.head()

export = test[['Id','Predictions']].rename({'Predictions':'SalePrice'},axis=1)
export.head()
Out[79]:
Id SalePrice
1452 1461 121472.388615
1453 1462 153338.843256
1454 1463 180796.158235
1455 1464 198507.705302
1456 1465 192062.391242
In [80]:
#export.to_csv(r'C:\Users\sjenkins\OneDrive - Dunelm (Soft Furnishings) Ltd\Documents\Side_Projects\House_Price_Regression\submission.csv',index='Id')

Summary

I'm really happy with what I've learnt in this project. Reading and making notes from other notebooks on Kaggle has been inspiring.

I'm also midway through Andrew Ng's Machine Learning Course, and have been able to apply my newly learnt understanding of Bias/Variance and Regularistation to the problem.

Other Avenues To Try (Inspired by other notebooks):

  • Building a neural network
  • Applying ensemble methods to aggregate my models.

To Further Practice Bias/Variance Understanding

Bibliography (Notebooks for inspiration):

END